so I'm pretty methodical about it now. What works for me is checking the series page on Amazon first—if it says "Read and Listen for Free" with Kindle Unlimited on the series listing itself, not just the first book, you're usually golden. I just finished all of Julie Klassen's 'Tales from Ivy Hill' that way; all three novels and the Christmas novella were included. Same with Allison Pittman's 'The Seamstress' trilogy. The real trap is when book one is free, book two is KU, and book three isn't in the program at all. I wish Amazon had a clearer filter for "complete series in KU."
For newer stuff, I've had luck with authors who publish wide in KU. Stella Riley's Rockliffe series is fully there, which is a steal because those are chunky, properly researched Regency novels. Same with D.K. Broster's 'The Flight of the Heron' trilogy—older books, but the whole series is available. I tend to avoid anything marked 'Series Starter' unless I physically check the other books' details. It's a bit of legwork, but finding a whole historical saga ready to binge is worth the preview-page scrolling.