I want to play a swashbuckler, and I saw the Gymnast and Tumbling Opportunist feats where you can tumble through and then trip as a free action. Do you get to keep the panache points from both?
There are no "points", you either have Panache or you don't.
The rules for Panache (relevant part quoted below from Archives of Nethys) only state that "you are either in a state of panache or you are not".
You care as much about the way you accomplish something as whether you actually accomplish it in the first place. When you perform an action with particular bravado, you can leverage this moment of verve to perform spectacular, deadly maneuvers. This state of flair is called panache, and you are either in a state of panache or you are not.