On a strictly house-rule scenario, I'd be inclined to allow Speak with Animals to affect magical beasts with intelligence of 1 or 2 (kinda like Wild Empathy).
You speak to the hippogriff in common, and you have to understand its body language. Start by respectuously bowing to the creature, hippogriffes are very proud and require politeness. Never insult them. If they bow back, you can pet them a bit, and if they react favorably, then you know they'll let you ride them. If they try to intimidate you, back away calmly but steadily, and leave them alone afterwards -- that way, you won't start a fight.
Or you can do like me and let speak with animals work on magical beasts with animal-like intelligence (1 or 2).
Yeah, as Gez and Klaus said, my DM allowed speak with animals to work. Of course, all it ever says is it's hungry. "Why have you not feed me? That small child would taste good..."