Kyogre

[XY Research]

Name: Kyogre
Type: Water
Ability: Drizzle
Base Stats: 100 / 100 / 90 / 150 / 140 / 90

Level-Up Movepool
(most likely)
???: Water Pulse

Start - Water Pulse
L5 - Scary Face
L15 - Body Slam
L20 - Muddy Water
L30 - Aqua Ring
L35 - Ice Beam
L45 - Ancient Power
L50 - Water Spout
L60 - Calm Mind
L65 - Aqua Tail
L75 - Sheer Cold
L80 - Double-Edge
L90 - Hydro Pump

TM & HM Compatibility
TM04 - Calm Mind
TM05 - Roar
TM06 - Toxic
TM07 - Hail
TM10 - Hidden Power
TM13 - Ice Beam
TM14 - Blizzard
TM15 - Hyper Beam
TM17 - Protect
TM18 - Rain Dance
TM20 - Safeguard
TM21 - Frustration
TM24 - Thunderbolt
TM25 - Thunder
TM26 - Earthquake
TM27 - Return
TM31 - Brick Break
TM32 - Double Team
TM39 - Rock Tomb
TM42 - Facade
TM44 - Rest
TM48 - Round
TM55 - Scald
TM68 - Giga Impact
TM73 - Thunder Wave
TM77 - Psych Up
TM78 - Bulldoze
TM80 - Rock Slide
TM87 - Swagger
TM88 - Sleep Talk
TM90 - Substitute
TM94 - Rock Smash
TM100 - Confide
HM03 - Surf
HM04 - Strength
HM05 - Waterfall

Egg Moves

 

[Wichu]

Got hold of a Kyogre, will update with movepool/TM compatibility in a few minutes. It's level 89 though, so I can't get levels for earlier moves. I'll Rare Candy it up to 100 and check if it learns anything then though.

EDIT: Level up:
???: Water Pulse
???: Scary Face
???: Body Slam
???: Muddy Water
???: Aqua Ring
???: Ice Beam
???: Ancient Power
???: Water Spout
???: Calm Mind
???: Aqua Tail
???: Sheer Cold
???: Double Edge
90: Hydro Pump

TM compatibility:
4: Calm Mind
6: Toxic
7: Hail
10: Hidden Power
13: Ice Beam
14: Blizzard
15: Hyper Beam
17: Protect
18: Rain Dance
20: Safeguard
21: Frustration
24: Thunderbolt
25: Thunder
26: Earthquake
27: Return
31: Brick Break
32: Double Team
39: Rock Tomb
42: Facade
44: Rest
55: Scald
68: Giga Impact
73: Thunder Wave
77: Psych Up
78: Bulldoze
80: Rock Slide
87: Swagger
88: Sleep Talk
90: Substitute
94: Rock Smash
100: Confide
H3: Surf
H4: Strength
H5: Waterfall

I'm missing TM05, TM34, TM43, TM45, TM48, TM51, TM59, TM60, TM64, TM67, TM72, and TM85. I'll work on getting those and testing them now.

 

[VioletPumpkin]

I obtained a Level 46 Kyogre. From leveling it to 100, checking the Move Relearner, and past games, its full level up list is most likely the following:

Start - Water Pulse
L5 - Scary Face
L15 - Body Slam
L20 - Muddy Water
L30 - Aqua Ring
L35 - Ice Beam
L45 - Ancient Power
L50 - Water Spout
L60 - Calm Mind
L65 - Aqua Tail
L75 - Sheer Cold
L80 - Double-Edge
L90 - Hydro Pump

Additionally, here's the complete list of TMs/HMs.
TM04 - Calm Mind
TM05 - Roar
TM06 - Toxic
TM07 - Hail
TM10 - Hidden Power
TM13 - Ice Beam
TM14 - Blizzard
TM15 - Hyper Beam
TM17 - Protect
TM18 - Rain Dance
TM20 - Safeguard
TM21 - Frustration
TM24 - Thunderbolt
TM25 - Thunder
TM26 - Earthquake
TM27 - Return
TM31 - Brick Break
TM32 - Double Team
TM39 - Rock Tomb
TM42 - Facade
TM44 - Rest
TM48 - Round
TM55 - Scald
TM68 - Giga Impact
TM73 - Thunder Wave
TM77 - Psych Up
TM78 - Bulldoze
TM80 - Rock Slide
TM87 - Swagger
TM88 - Sleep Talk
TM90 - Substitute
TM94 - Rock Smash
TM100 - Confide
HM03 - Surf
HM04 - Strength
HM05 - Waterfall