In spite of what
Dece1t said, technically Mega Gyarados does not share a type with Flying teams. Mega Gyarados's typing is Water / Dark, something you simply cannot argue. If you have a Monotype team based around Flying-type Pokemon, does it make sense to have a Water / Dark Pokemon on the team? Mega Gyarados has no Flying elements at all, given that it is not immune to Ground-type attacks and does not get protected by Delta Stream, so it doesn't make any sense for it to be considered a Flying-type Pokemon.
For a more mechanical understanding, let's temporarily consider Monotype Balanced Hackmons, an OM that used to be played occasionally. For the record, Balanced Hackmons requires cartridge compliance, so anything that can be done in Balanced Hackmons can technically be done on the real ORAS games. In Balanced Hackmons, Mega Evolutions are usable without the prior use of a Mega Stone to Mega Evolve. This means you can use a Mega Gyarados with any item, such as Choice Band, if you so pleased. In Monotype, by the Same Type Clause, all Pokemon must share a type, and a Flying team in Monotype Balanced Hackmons could not use Mega Gyarados even under the current ORAS rules. Thus, I'd argue that Mega Gyarados is by definition not a Flying-type Pokemon and should not be legal on Flying teams.
Are there reasons that Gyarados's Flying typing should legalize Mega Gyarados by proxy other than "This is how it's been done before" or "It's more fun"? Neither are compelling, as the first is contrary to progress and the second is completely subjective. Also, just as our tiering philosophy does not favor one type over another, the foundational rules of the metagame should not made with the mindset of making any one X type more usable.
(I'll make some super small post-note that the fact that you can even use Mega Gyarados without a Mega Stone on cartridge is minor evidence that it should be considered a separate Pokemon and should not be grouped together with Gyarados for typing purposes)