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Without a timer, if your stream can be found in a url form just save a link on your homescreen. One click can start it.

For a one button solution with timer if no app is satisfactory you can build your script in Workflow (IOS) or any other automation tool on android. You might find a script already made on your liking.

I mention radiodroid elsewhere here: it has a sleep timer that defaults to the last one set, so you would have to tap first to start the app, then 2nd to start a station (at the top of your favorites), then the timer and ok, so that is 4 taps I guess.

Edit: and it seems, an alarm clock.

Try IFTTT or Automate.