What app can mute media when I flip the phone display screen facing downwards/floor?

Have you looked at automation apps like Tasker or Macrodroid?

 

The media app itself may very well have a setting for what you want it to do during a phone call or other notification.

 

Tasker, mentioned above, has a "face down" profile state which can be assigned tasks.

 

Macrodroid will help you in that case!

 

I thought this

I thought this was interesting, and created a Tasker profile as "state - orientation face down", and the task assigned to that state was media command pause, see screencap, works like a champ.