Depends. Historically all of them but the Green flight have been dipping their toes everywhere. I can't see any flight besides the green one aligning itself entirely with one faction, unless you're basing it off of solely one character or colors.
Blue - Are attracted to magic/power. They'll go where magic is bountiful which is on the Horde side, but the Alliance has a biased Dalaran and some returning magic elves. The Alliance and Horde also both have powerful magic users, even if Jaina is the token mage for the story.
Red - They have a terrible history with orcs, but that was somehow mostly pinned onto Garrosh and orcs that sided with him (who we killed). Then again, they seem to have favored Thalassian culture and are similarly snappy/aggressive despite still having an association to nature/healing.
Black - They have a lot of drama going on with human kingdoms, but their only two "leaders" are heavily biased in two different directions. Wrathion is Anduin's best friend and dubious advisor, while Ebonhorn is Mayla's advisor and is openly a part of the Horde because of his loyalty to the High Mountain. I can't see any other remaining leaders like Sabellion wanting much to do with either faction or motal races in general.
Bronze - They have the widest variety of forms and put their mission above mortal factions. They'll ask anyone and everyone to help when they need it, regardless of the politics so idk. They're the most true neutral by far.