The Sonos Roam has bluetooth and can share it’s bluetooth audio  (group) with other Sonos speakers in your setup.  That sounds like it might work for you. 

https://support.sonos.com/en-us/article/share-roam-s-bluetooth-audio-with-your-sonos-system

Not sure what you mean by an “interval timer”. Could this be something like an alarm? 

Maybe the sleep timer that might work for you? You’d start playback of your desired play list, then set a sleep timer for the desired length that you want the workout to last, and the Sonos would stop at that length of time.  

So if I bought a wireless Bluetooth roam speaker for the gym I could use the Bluetooth off that paired with the speakers and amp at the gym and run off Bluetooth ?

Technically it would be “grouped” not paired.  The timing might not be 100% perfect with this setup, but I think it would be good enough for what you want to accomplished.

I think the idea is that you would setup the timer so that it would be 1 minute of planks, 30 seconds rest, 1 minute of sit-ups, 30 seconds rest….that sort of thing.  So a simple alarm really wouldn’t cut it.  Back when I was a younger man, whoever was instructing would have to watch the clock and yell out when it was time to switch, but I can see where getting this more automated, maybe even switching music when you move to the next exercise or whatever, would help make it interesting. 

If you have enabled Alexa, you can “set timer for …”. I have not investigated the idea of multiple timers. And, a nag is that you must “stop timer” or Alexa will keep reminding you that the timer has expired.