I use Flow for work professionally. I find that sometimes the keyboard doesn't switch properly as fast as the mouse and I end up typing on the wrong screen. I have ideas on how to remedy this.

Hardware Option1: The Keyboard/mouse should have a master/***** receiver that you can plug the others receiver into, so it essentially makes one of them the master, so if you hit button 2 on keyboard, it will switch mouse AND keyboard instantly... or vice versa with mouse.

Software Option2: Add an option into flow that determines if either the mouse or keyboard is the "master" device. Say we set mouse to master. Then when we hit "2" on mouse, the keyboard will also switch to 2 instantly. This is an easier add, and would/should fix glitches with CTRL+mouse off screen getting stuck sometimes. I suppose it can be an if statement also instead of a master device...
if <device input> on mouse changed, then set <keyboard> to same value, else if <device input> on keyboard changed, then set <mouse> to same value.
This would make it so all will work, but if something is switched over... both switch over, which would be way better.