yeah, I had to check before hand, because I had previously used the Amazon free trial (and sometimes paid) for Showtime and Cinemax, and I only recall doing it at the end of seasons that I want to watch....and know that those are released a few hours to a day late. ....but they all have the "live option" when you scroll to the bottom of the channel menu. I never used it before, but then googled about that for Amazon HBO, before jumping on it yesterday ahead of GoT...but it worked tonight. Just leave it on the main live HBO channel and it plays through. No pause though, of course.
The various premium channel subs through Prime are usually $10 or $15 per month (I think only HBO is $15?). So, I wait until there are a couple of shows, maybe with multiple seasons that I want to binge or catch up on, then I grab them for a month. Worked so far.