Flavors are only used at instance launch time (and when resizing), thus it only affects instances that you launch after deleting the flavor.

Now, stacks often implement autoscaling, which means the deleting and creating of instances according to the application's load. Such a stack will definitely be impacted by a missing flavor.

If you take care to recreate the flavor with the same name as the old one, and to be safe, also the same ID, there should be no problem for such stacks either. Except if the stack decides to create an instance right after you remove the flavor and before you recreate it.