I have exactly the same problems when using ZWIFT and my Flux 2, which Computer/ Platform are you using? (In my case its IOS with an iPad)
Edit: this was the reply I got from ZWIFT support in April 2019, however these things didn’t help in my case (already had the latest firmware, recalibrated the trainer, placed the iPad next to the trainer for testing purposes):
I’m sorry to hear you’re having issues with your trainer. I’d like you to try updating the firmware on your trainer to see if this resolves the issue.
Instructions for updating your trainer’s firmware should be available on your manufacturer’s website, and we list information for some brands on our knowledge base.
After updating your firmware it’s a good idea to calibrate your trainer as well. Calibration for some trainers can be done in Zwift. Instructions on our knowledge base article “How to calibrate your trainer,” and most manufacturers provide a mobile app that you can use to do this as well.
This could possibly also be caused by a Bluetooth signal drop. We’ve written a guide describing common potential interference sources, in the article “My Bluetooth signal is Dropping,” so you can try and eliminate them.
Give that a try, and let me know how it goes.