Infernape was a monstrous wallbreaker in Gen IV, when Skarm-Bliss, Suicune, Milotic, and others were common on teams everywhere. Blaziken was basically the poor man's Fire-Fighter, relegated to the tier below. Then Gen V came and the positions were absolutely swapped, even moreso because Blaziken is uber now. But Infernape still sees action in Doubles, especially because of its fast Fake Out.
Infernape owns a fine collection of moves, and it finds difficulty including much of its arsenal with the essentials. It's tempting to try to run it mixed, because of what its stats suggest and because that was traditionally its role, but Doubles is a "broad" metagame where one Pokemon does not have to attack one other Pokemon. Like most Pokemon in Doubles, it is very dependent on its allies, and shouldn't be butchering its stats to try and take care of every threat.
Infernape #392
HP: 76
Atk: 104
Def: 71
SpA: 104
SpD: 71
Spe: 108
->Physical<-
Infernape @ Flying Gem / Focus Sash / King's Rock
JOLLY
+Blaze+
6 HP / 252 Atk / 252 Spe
-Fake Out
-Close Combat
-Acrobatics / Blaze Kick / Shadow Claw / Stone Edge
-U-turn / Taunt / Protect / Fling
Close Combat and Acrobatics provide practically perfect coverage (Only resisted by regular Rotom, I think). The unfortunate thing is that the frail Infernape must give up its Focus Sash in order to function effectively at all with Acrobatics. Fighting and Flying together cover all the types that Fire would hit supereffectively, and since the moves are already competing for a slot it isn't the main option, in spite of being a powerful STAB to have. U-turn, Taunt, and Protect are roughly equal; Protect is more an option for Focus Sash, so Infernape can Protect when at 1 HP while its partner KO's the foe's eager priority-user. Fling is of course only for King's Rock, an option if you are paranoid about Ghost-types or need two turns of flinching.
As mentioned before, Acrobatics is preferred over Blaze Kick ordinarily, but even when using Focus Sash you might want to use Shadow Claw (for perfect coverage or Stone Edge, which hits harder but hits fewer Pokemon that resist Fighting. Rock Slide is another option that isn't specified because it seldom KOs what it needs to, and Infernape is a Pokemon that very much wants to KO it opponents before they get to him rather than provide flinch support, but if that's the role you need it to do then try it out.
->Special<-
Infernape @ Focus Sash / Life Orb
TIMID
+Blaze+
6 HP / 252 SpA / 252 Spe
-Fake Out
-Heat Wave
-Grass Knot / SolarBeam
-Vacuum Wave / Hidden Power [Ice] / U-turn / Focus Blast
Infernape still wants Fake Out, but has turned Special otherwise. Heat Wave is the general mode of attack, and Grass Knot hits Water/Ground/Rock-types that would otherwise antagonize him (Though Rotom-W is basically immune to it). The last moveslot is the toughest. Vacuum Wave is nifty but doesn't do much type-wise. HP Ice takes care of Dragon- and Flying-types and Landorus if he decides to show up. U-turn is there for keeping the momentum on your side, especially if you're up against something you hit supereffectively and you want to safely find out the rest of the foe's party.
This is also the preferred set for Drought teams, with some changes. Supposing you don't have a strong Grass-type to bring in when you know it will be sunny (And thus SolarBeam is a safe option), SolarBeam can replace Grass Knot as a max-powered Grass-type move. Hidden Power [Ice] also KOs many strong foes that Drought teams have trouble with; even if Ninetales carries it, it won't be enough to KO many 4x weak Pokemon off of Ninetales' relatively weak SpA. If if IF you absolutely need a Fighting-type move and Infernape seemed like the perfect solution (Fire/Fighting-type) for a Drought team, Focus Blast can help a little. Don't expect to OHKO Chople-tar with it or anything, even if it actually freakin hits it.
---------------------------------
Might write up a mixed set in a minute. What do y'all think?
Infernape owns a fine collection of moves, and it finds difficulty including much of its arsenal with the essentials. It's tempting to try to run it mixed, because of what its stats suggest and because that was traditionally its role, but Doubles is a "broad" metagame where one Pokemon does not have to attack one other Pokemon. Like most Pokemon in Doubles, it is very dependent on its allies, and shouldn't be butchering its stats to try and take care of every threat.

Infernape #392
HP: 76
Atk: 104
Def: 71
SpA: 104
SpD: 71
Spe: 108
PHP:
Level-Up Moves
-- Scratch
-- Leer
-- Ember
-- Taunt
Lv7 Ember
Lv9 Taunt
Lv14 Mach Punch
Lv16 Fury Swipes
Lv19 Flame Wheel
Lv26 Feint
Lv29 Punishment
Lv36 Close Combat
Lv42 Fire Spin
Lv52 Acrobatics
Lv58 Calm Mind
Lv68 Flare Blitz
Machine Moves
TM01 Hone Claws
TM04 Calm Mind
TM05 Roar
TM06 Toxic
TM08 Bulk Up
TM10 Hidden Power
TM11 Sunny Day
TM12 Taunt
TM15 Hyper Beam
TM17 Protect
TM21 Frustration
TM22 SolarBeam
TM26 Earthquake
TM27 Return
TM28 Dig
TM31 Brick Break
TM32 Double Team
TM35 Flamethrower
TM38 Fire Blast
TM39 Rock Tomb
TM41 Torment
TM42 Facade
TM43 Flame Charge
TM44 Rest
TM45 Attract
TM47 Low Sweep
TM48 Round
TM50 Overheat
TM52 Focus Blast
TM56 Fling
TM59 Incinerate
TM61 Will-O-Wisp
TM62 Acrobatics
TM65 Shadow Claw
TM67 Retaliate
TM68 Giga Impact
TM71 Stone Edge
TM75 Swords Dance
TM78 Bulldoze
TM80 Rock Slide
TM83 Work Up
TM84 Poison Jab
TM86 Grass Knot
TM87 Swagger
TM89 U-turn
TM90 Substitute
TM94 Rock Smash
HM01 Cut
HM04 Strength
Pre-evolution Moves
Nasty Plot (Chimchar only)
Slack Off
Egg Moves
Assist
Blaze Kick
Counter
Double Kick
Encore
Fake Out
Quick Guard
Fire Punch
Focus Energy
Focus Punch
Heat Wave
Helping Hand
Submission
ThunderPunch
Gen IV Tutor Moves
(D/P/Pt/HG/SS) Blast Burn
(Pt/HG/SS) Endeavor
(Pt/HG/SS) Fire Punch
(Pt/HG/SS) Gunk Shot
(Pt/HG/SS) Heat Wave
(Pt/HG/SS) Helping Hand
(Pt/HG/SS) Mud-Slap
(Pt/HG/SS) Rollout
(Pt/HG/SS) Snore
(Pt/HG/SS) Swift
(Pt/HG/SS) ThunderPunch
(Pt/HG/SS) Vacuum Wave
(HG/SS) Headbutt
(HG/SS) Low Kick
(HG/SS) Magic Coat
Infernape -> Double Battles
->Physical<-
Infernape @ Flying Gem / Focus Sash / King's Rock
JOLLY
+Blaze+
6 HP / 252 Atk / 252 Spe
-Fake Out
-Close Combat
-Acrobatics / Blaze Kick / Shadow Claw / Stone Edge
-U-turn / Taunt / Protect / Fling
Close Combat and Acrobatics provide practically perfect coverage (Only resisted by regular Rotom, I think). The unfortunate thing is that the frail Infernape must give up its Focus Sash in order to function effectively at all with Acrobatics. Fighting and Flying together cover all the types that Fire would hit supereffectively, and since the moves are already competing for a slot it isn't the main option, in spite of being a powerful STAB to have. U-turn, Taunt, and Protect are roughly equal; Protect is more an option for Focus Sash, so Infernape can Protect when at 1 HP while its partner KO's the foe's eager priority-user. Fling is of course only for King's Rock, an option if you are paranoid about Ghost-types or need two turns of flinching.
As mentioned before, Acrobatics is preferred over Blaze Kick ordinarily, but even when using Focus Sash you might want to use Shadow Claw (for perfect coverage or Stone Edge, which hits harder but hits fewer Pokemon that resist Fighting. Rock Slide is another option that isn't specified because it seldom KOs what it needs to, and Infernape is a Pokemon that very much wants to KO it opponents before they get to him rather than provide flinch support, but if that's the role you need it to do then try it out.
->Special<-
Infernape @ Focus Sash / Life Orb
TIMID
+Blaze+
6 HP / 252 SpA / 252 Spe
-Fake Out
-Heat Wave
-Grass Knot / SolarBeam
-Vacuum Wave / Hidden Power [Ice] / U-turn / Focus Blast
Infernape still wants Fake Out, but has turned Special otherwise. Heat Wave is the general mode of attack, and Grass Knot hits Water/Ground/Rock-types that would otherwise antagonize him (Though Rotom-W is basically immune to it). The last moveslot is the toughest. Vacuum Wave is nifty but doesn't do much type-wise. HP Ice takes care of Dragon- and Flying-types and Landorus if he decides to show up. U-turn is there for keeping the momentum on your side, especially if you're up against something you hit supereffectively and you want to safely find out the rest of the foe's party.
This is also the preferred set for Drought teams, with some changes. Supposing you don't have a strong Grass-type to bring in when you know it will be sunny (And thus SolarBeam is a safe option), SolarBeam can replace Grass Knot as a max-powered Grass-type move. Hidden Power [Ice] also KOs many strong foes that Drought teams have trouble with; even if Ninetales carries it, it won't be enough to KO many 4x weak Pokemon off of Ninetales' relatively weak SpA. If if IF you absolutely need a Fighting-type move and Infernape seemed like the perfect solution (Fire/Fighting-type) for a Drought team, Focus Blast can help a little. Don't expect to OHKO Chople-tar with it or anything, even if it actually freakin hits it.
---------------------------------
Might write up a mixed set in a minute. What do y'all think?