Is it possible for me to make a certain Spawnset auto kit for a certain player only by say granting them a permission or something?

I want all my players to spawn with the Default Spawnset I created but then I also want to be able to create a Kit that only select players with a certain permision will get every time on respawn instead of the Default auto kit. Is this possible?

Yes, you can do this via the Custom Auto Kits plugin: https://umod.org/plugins/custom-auto-kits. Note that while the plugin is not currently maintained, this functionality still works.