There's something about Flygon and Salamence that I don't get. Is there really an actual rivalry between them as said by the Pokémon Company or was that suggested by some fans?

I don't believe there is a rivalry that is spelled out by the Pokémon company itself more on the effect of what we've seen from different dragon type Pokémon interacting with each other. From the anime's perspective Dragon type Pokémon (Mind you this is as far as I'm aware and I could be wrong.) Are powerful Pokémon that do not tend to like being around each other and see each other as a threat which may also have basis in the sense that dragon-type is weak/strong to dragon-type.

Hmm, I see. Interesting.