Logitech flow looks interesting. From the 30 seconds I scanned the page about it, it seems the computers need to be on the same network. So this could be as "simple" as running tcp client on each machine. When the current active machine notices that the mouse left the edge of the current screen it disables the keyboard and mouse on current machine, sends a notification to the other computer and enables keyboard and mouse there. Custom USB drivers could likely handle disabling and enabling the keyboard and mouse just fine, but I've never written one, so maybe I'm wrong.

Edit: I was speaking more generically here. I doubt one could get the actual Logitech mouse and keyboard protocol and so couldn't implement an open source flow clone.