As (likely) the biggest Flygon fan on this forum, I'd be remiss to not contribute here. I have a couple of routes that a theoretical Mega Flygon could take; I've listed them, along with respective pros and cons, below. I've also taken into account all the currently-existing Megas, so as to not tread too close to existing designs.
For all sets, Flygon's base stats are: 80/100/80/80/80/100, BST 520. Per the rules of this thread, I have 100 additional stats to distribute, for a Mega BST of 620, and per the in-game rules, HP cannot be changed.
Concept 1: Special Dragon/Bug with Tinted Lens
Mega Flygon (Dragon/Bug)
Ability: Tinted Lens (Doubles power of all NVE attacks, effectively making single-resisted moves hit neutrally, and making double-resisted moves hit for half damage).
Mega Stats: 80/110/85/140/95/110
Concept: This Mega Flygon concept takes a similar route as Mega Pidgeot, taking a Pokemon previously seen only as a physical attacker and giving it a heavy boost to its Special Attack. Flygon has always been somewhat cursed with having a better special movepool than physical, despite its typing and stat spread, and the addition of rare and powerful Special moves like Bug Buzz and Boomburst to its arsenal in ORAS lend credence to a special-attacking Mega with typing to take advantage of it (a real-world example can be found in XY Swablu, which suddenly could learn Moonblast by level up, before its Fairy-type Mega was revealed). Between the special attack boost and the effect of Tinted Lens dramatically lowering the number of potential walls, this Flygon could prove to be a real threat, with a number of strong Special moves like STAB Dragon Pulse/Draco Meteor and Bug Buzz, Earth Power, Fire Blast, Boomburst, and Giga Drain at its disposal. Tinted Lens, of course, also works on this Mega Flygon's Physical attacks, namely newly-STAB U-Turn, surprise Outrage for special walls, and Rock attacks.
Concept 2: Speedy Dragon/Bug with Sand Rush
Mega Flygon (Dragon/Bug)
Ability: Sand Rush (Doubles Speed during Sandstorm weather effect. Speed does not double on turn it activates.)
Mega Stats: 80/125/85/125/90/110
Concept: This variant uses a more balanced stat spread than the first design. It would play more like how regular Flygon currently operates; using speedy (often Scarfed) U-Turn to weaken counters. The U-Turn of this Mega Flygon, even with STAB, would still be much weaker than that of Mega Beedrill, but has the advantage of having a better Pokemon before Mega-evolving, and for better overall bulk for surprise/priority attacks. Because there are already two Megas with the Sand Force ability (one of course being the ever-present, same-typed nemesis Mega Garchomp), I took a different route; capitalizing on Sandstorm's presence with a massive boost to Speed. With Sandstorm up, this Mega Flygon would outspeed most everything, making it a lethal revenge killer and momentum-gainer with STAB U-Turn. The modest boosts to both of Flygon's attacking stats give it the opportunity to run physical, special, or mixed moves for the best possible neutral coverage alongside that terrific speed in sandstorm.
I'll add more later.
-sandragon13
Be sure to check out my Otaru Regional Fakedex. Updating regularly with new Fakemon. Always looking for feedback!