How can I set a flag to be flagged unlimited number of times? I have a flag on a node that anyone can flag. The flag is tied to a Rule that executes an action. Essentially I need to be able to allow any user to flag a node as many times as they wish and track the flag count.

The problem: It appears that with the Flag module, the flag needs to be unflagged for the user to be able to flag it again. This essentially makes the flag count pointless as they are adding, removing and re-adding the same flag over and over.
As Triskelion mentioned, the Flag module might be the wrong tool for your use case. Despite that, if you're looking to allow multiple flagging (instead a flag/unflag toggle) you can add a Unflag a Node action (or whatever your flagged entity is) to the other action you have on a flag event.