[@Reflection]yeah, the Dratini line is about it for gen 1 and 2, though the Charmander line an Gyrados could fit too.

As the premise is that the King brought together people who had worked for him, the Queen, and his council, I'm not sure how well a mercenary would work.  A "Royal Dragon Knight" would fit much better thematically, as he would like to send a Royal bodyguard with his son.