Sorcerers require teachers in the Dragonlance setting. I’m fine with that too. In this instance, it’s training to access magic in a way different to wizards.
In the Dragonlance setting, in the Age of Mortals (3E), one can become a Sorcerer if another Sorcerer teaches, assuming they have a Charisma score high enough to cast spells. Palin Majere teaches sorcery at the Academy of Sorcerery, and there is also a very cool Sorcerer prestige class called the academy sorcerer connected with that. It’s also possible to learn to be a sorcerer 1 to 1.
As I mention upthread, if you are taking the materialist approach to magic, then it makes it difficult to countenance creatures with innate magical ability (although the nightmare beast is one such example). So just change the fluff. The idea is to convert Dark Sun to 3.5E, not convert 3.5E to Dark Sun.