You ask, are the carrying capacity rules for flying creatures the rules the same as for anyone else.
Good question. The book doesn’t say.
What you’re really asking is are the carrying capacity rules for flying the same as for not flying? The carrying capacity rules are perhaps intended for carrying while walking, and even so, as you pointed out, they’re not necessarily perfectly reasonable.
So, yes, the carrying capacity rules for flying characters are the same as for other characters. When they’re walking, they can carry their strength times 15.
But what about when they’re flying? There’s no rule for that.
To come up with any answer to the question in your title, “How much weight can an Aarakocra carry when flying?” would require substantial speculation.