So according to Bulbapedia, Blaziken may have various cultural allusions, ranging from the bird-headed sun deities Horus and Ra from Egyptian mythology, to the phoenix, to fire-breathing chickens and bird-headed humanoids of Japanese folklore. Do you think there’s any credibility to this? Personally I think Horus/Ra might be reaching but they might be on to something with the basan/karura.

Well, I’m super vague on some of those things, but I don’t think Blaziken needs to be all of them.  I think if there’s a fire chicken in Japanese folklore, and if we know that cockfighting is a real thing that makes the additional Fighting type appropriate, well, you’ve sort of got the whole design there; there’s not really any more mystery to what Blaziken is and does that we need to find explanations for.  Like, you can say “well, on top of all that it’s similar to Horus” but I think if the designers meant it, there would be some more specific call-out for us to pick up.