Can I use sand mix dry to fill in the cracks on my flagstone patio? I'd like to broom it in and then lightly mist it

You can but limestone screening works even better. There is a special sand with a small amount of concrete mixed in sold specifically dodo what you want. The trouble with sand is you may lightly mist it but mother nature won't. Big rains will wash sand out.

By sand mix do you mean a cement sand mix? If so, then the answer is yes.