If I quit a job that is a member of a certain franchise how long must I wait before I can get a job with a different company of the same franchise

I suggest you not quit your job until you have an experienced lawyer review any covenants not to compete in contracts you signed,  the territory of those covenants, and the reasonableness of those covenants.  I also suggest that you not take any customer lists or unpublished data or material in your possession even if you created the data or material.