Here's how dragon racing and Brian Griffin enters the series in The Day the Griffin's Came Part 1.
[We see Equestria is having dragon racing]
Pinkie: [through mircophone] And there goes Skyla and Crystal Heart! They're going around the bend with a magificate speed! But wait, what's this? It's Fishlegs and Meatlug!
[Fishlegs and Meatlug then start catching up with Skyla and Crystal Heart and then start to over take them.]
Pinkie: [through microphone] Fishlegs is almost making it!
[Fishlegs crosses the line]
Pnkie: [through microphone] And the winners are Fishlegs and Meatlug!
[the racers then land]
Fishlegs: We did it, buddy!
Skyla: [looking out to the open]
[when Nightstar and Yuna land, Yuna hops off and goes over to her]
Yuna: Hey, Sky, what's on your mind?
Skyla; Well, it's not about loosing the race. It's just. What if someone is killing dragons?
Yuna: [giggles] That's silly. Everyone knows that dragons are friends now.
Brian: [off screen] HAAAAAAAAAAAAA!!!!!
[We seeing Brian killing dragons]
[we are now in the ruins of Quahog]
Brian: Heracross, use hyper beam!
Heracross: [builds up energy] Hera.... [uses it on dragons] CROSS!!!!!!!!!!!
[several dragons are killed by Heracross' hyperbeam]
Vinny: We're getting flaged! [fires a DC-15A blaster rifle] Brian, Heracross! Come back!
Brtian: Come on Heracross!
[they then race in just in time before the doors closed]
Brian: Good job, Heracross. Return!
[Heracross goes back into his PokeBall]
Peter: This is becoming too intense!
Quagmire: We already lost several men.
Stewie: My flight squad's been blown out of the sky.
Cleveland: And most of my squadarn was killed!
Meg: We'll never beat all these dragons!
[Everyone then starts arguing]
Brian: There's one hope. Equestria.
Brian: Yes, if we talk to the royal family, they might be able to help us out.
Peter: I don't know about that.
Brian: Look, Peter! I seen Princess Celestia raised the Sun everyday, and Princess Luna raising the Moon everynight! Before all of this happened. We're going to Equestria, to rebuild our home!
Brian: Come along! To Equestria we go!
[Everyone heads to the boats and sailed off]