See, All India of Medical Sciences or AIIMS are central medical institutes, and do not offer any kind of quota or discriminates on the basis of your domicile, just as IITs. So, if you belong to the Jammu and Kashmir domicile and want to get admission into let's say AIIMS Delhi, then you're free to do so.

Not only for J&K, but any student from any part of India can study in any AIIMS spread all over the country.

Hope I have answered your question. All the best!