The extra hit dice are d10s because they are Magical beast hit dice. You can't substitute class hit dice instead.
Note that the Call Flying Mount class feature outlines that the flying mount must be a Celestial Giant Eagle, Celestial Giant Owl, or Celestial Pegasus, all of which are magical beasts.
Unfortunately, unlike a Paladin's mount, the Flying Mount from this ability doesn't gain extra skill points or feats for having those extra hit dice per the RAW.
I've always house-ruled that out though, and you may be able to talk your DM into allowing it to get skills and feats for its hit dice.
If your DM allowed a Flying Mount not of the magical beast type (that is, if it wasn't a vermin or animal type), it might have a different hit die type.