To qualify for that feat, you need the ability to cast an Arcane spell. That pretty much says "This is a feat for Bards", as it's the only class that casts arcane spells and doesn't get a Familiar. All the PRCs that give Arcane casting ability are based on an arcane caster as the base class.
As for getting an extra familiar with "Obtain Familiar", it references the Sorcerer and/or Wizard class. These have a particular requirement for obtaining a familiar: You can't currently have one.
As for Dragon: There have been a lot of things written up there over the years that never actually made it into the rules, and shouldn't have. There were half a dozen different class write ups for Ninja, before Oriental Adventures came out. None of them matched the actual class that ended up in the RAW.
So while the DM might have allowed any/all the books, that might not include Dragon. Find the article, so you can show him exactly what the rules and limitations are, and then make your pitch.