Hi Terry,
I agree with what "Tootles" is saying. If a TV is a "smart TV" and has built-in online capabilities, more than likely it will be able to decode the video file from the flash drive and play it. However, many older TV's also contain USB ports for the purpose of diagnosis and updates and have no ability to play video files from them. Possibly ask the gym manager if their TVs can accomplish what you would like to do; I'm sure they'd be happy to let you know whether you have their permission to try it!