To put it bluntly, no, Pyroar would not be viable against Flutter Mane or in any mainstream format containing it.
Flutter Mane frequently runs Power Gem, which is a guaranteed OHKO. Even without Power Gem, Moonblast or any common coverage move is a guaranteed 2HKO. Because Flutter Mane easily outspeeds Pyroar, it's unlikely that Pyroar will come out on top.
It's kind of odd to have a Pyroar with the Sp. Def allocation in your example. Pyroar's defensive stats are too poor to be worth investing in, since it'll still get wiped out fairly easily (especially in a format that allows the likes of Flutter Mane), so it usually invests in Sp. Atk and Speed to make use of its best (but ultimately still mediocre) stats. Here are some damage calculations with a Pyroar that doesn't have defensive EVs:
- 252 SpA Choice Specs Flutter Mane Power Gem vs. 0 HP / 0 SpD Pyroar: 378-446 (120.7 - 142.4%) -- guaranteed OHKO
- 252 SpA Choice Specs Flutter Mane Moonblast vs. 0 HP / 0 SpD Pyroar: 168-198 (53.6 - 63.2%) -- guaranteed 2HKO
- 252 SpA Life Orb Flutter Mane Thunderbolt vs. 0 HP / 0 SpD Pyroar: 185-218 (59.1 - 69.6%) -- guaranteed 2HKO
- 252 SpA Pyroar Fire Blast vs. 0 HP / 4 SpD Flutter Mane: 123-145 (49 - 57.7%) -- 96.1% chance to 2HKO
Flutter Mane is ranked as B in Ubers' viability rankings, whereas Pyroar currently sits at a B in ZU's viability rankings, representing an extremely disparate difference in power. Even if Pyroar countered Flutter Mane, a decent opponent would just switch out, since Pyroar would not be able to stand up to most of the other common threats in a format that allows Flutter Mane. You mentioned Miraidon–now why would it use Dazzling Gleam when it could just outspeed and...
- 252+ SpA Choice Specs Hadron Engine Miraidon Electro Drift vs. 0 HP / 0 SpD Pyroar in Electric Terrain: 672-792 (214.6 - 253%) -- guaranteed OHKO
Pyroar is a pretty poor Pokémon in general; it's held back by an awkward stat allocation, a lack of good abilities (Moxie as a Sp. Attacker...), a weakness to Stealth Rock, and by just being generally outclassed by many other Fire-types. For every strength it has, there are numerous other Pokémon who can do it better, especially in a format that's unrestricted enough to allow Flutter Mane.
This is actually a good example of how comparing Pokémon by their typings in isolation doesn't give a good picture of who has the upper hand.