The Flux S should definitely support long cage derailleurs (it’s the reason why I bought one over the discounted original Flux - I have a MTB with a long cage derailleur mounted to it). The original Flux (still a smart trainer) doesn’t support it because it hits the front legs of the trainer, much like in your picture. The Flux S body was specifically updated to accommodate long cage derailleurs by changing the leg design while maintaining the same internals as the final version of the original Flux. Your trainer looks more like pictures of the original Flux than the Flux S I have in my basement. For one, there’s a bolt on the raised piece right in front of your derailleur on my Flux S that doesn’t appear on yours and wasn’t on the original Flux either from what I can tell from pictures. This is what my Flux S looks like from the drive side:
If you need a shorter derailleur cage, most groupsets should have smaller cage options (either small or medium cage), but you’ll just need to make sure that you use a compatible cassette. The specs for the derailleur should tell you the max compatible cog size and you’ll just need to use a cassette that’s largest cog isn’t bigger than that. If you’re going to be getting a dedicated trainer bike, then that should be no issue, but if you’ll be using the bike on the road, you’ll just want to make sure the range will work for you. Alternatively, you might be able to just use your existing setup and not shift into the gears that result in rubbing.