So what are the most common offensive Flying type threats that actually use Flying STABs. I count Talonflame, Mega Pinsir, Gyarados (Bounce kinda exists), Tornadus-T, Mega Aerodactyl, Staraptor. The majority of these pokemon use physical STAB, which is a testament to the fact that Air Slash and the unreliable Hurricane are the only useful special Flying attacks.
I'd like to talk about some of the checks and counters to these pokemon. I don't know much about Tornadus or Mega Aerodactyl and Gyarados only rarely runs a set with Bounce so I'll focus on the other three: Talonflame, Mega Pinsir, Staraptor, the infamous Bird Spam core. I'll focus on pokemon that can at least somewhat wall all three of the birds.
Physically Defensive Rotom-W is a hard counter against Talonflame and Mega Pinsir (after it Mega Evolves.) A healthy Rotom can eat priority Brave Birds and Aerialte Returns from CB Talonflame and Mega Pinsir without a problem and can kill Talonflame with Hydro Pump and cripple Pinsir with Will-o-Wisp. Rotom does however have to be careful with Mold Breaker Earthquake from a Pinsir prior to Mega Evolution. Rotom also has the added advantage about not giving a shit about BU Talonflame, which many of the CB Talonflame counters such as Tyranitar hate. Rotom does not deal with Scarf Staraptor very well, because Double Edge easily OHKO's it. Additionally, Staraptor is most often used to punch holes in Talonflame or Pinsir's walls and thus it isn't a good idea to allow it to wear down Rotom.
Physically Defensive Zapdos also does a decent job walling Talonflame (not perfectly since Flare Blitz hurts) and Pinsir. It can even Roost off any damage that it takes switching in (as long as Rocks are not up) and can even deal with Staraptor to an extent because Double Edge only has a small chance to 2HKO. The big problem with using Zapdos as a counter is Stealth Rock prevents it from doing its job at all, and it often needs a decent amount of health to do its job as a defogger, which is its main role on most teams. However, teams that are facing 2 or 3 of Talonflame, Pinsir or Staraptor probably shouldn't want to Defog very often as keeping Stealth Rock on the other side of the field is vital.
Bulky versions of Landorus-T that run Stone Edge are also great switch in's to these Pokemon. Intimidate works wonders as it completely neuters all three birds and Stone Edge easily OHKO's. Additionally, switching in Landorus-T almost guarantees a switch out from the opposing bird and Landorus can use U-Turn to grab the momentum from the opponent. Using Physical Rotom and Landorus-T to form a VoltTurn core gives you a very favorable matchup against BirdSpam.
Skarmory deals well with Pinsir and Staraptor and CB Talonflames that are locked into Brave Bird. Using a Rocky Helmet makes the latter two almost kill themselves when they attack.
Gliscor running a Toxic and Roost and Slowbro running Toxic/Slack Off are checks as they can stall out the birds.
It's possible that I've missed out some pokemon but these are all the checks I can think of at the moment. Looking at this list, Life Orb Latios with Draco Meteor/Psyshock/Thunderbolt/Defog seems like a great partner for a BirdSpam core. It provides invaluable Defog support, deals with Slowbro and Skarmory with Thunderbolt, deals with Rotom-W and Landorus with a combination of any attack + Draco Meteor (or severely crippling them with just Draco Meteor), and OHKO's Gliscor with Draco Meteor. Additionally, it doesn't take much damage back from any of the checks.