ip6 won't boot after screen replacement unless I unplug Home flex.

Replacing the home button assembly will cause touch ID function to cease working but the home button function will still work.

Replacing the long home button flex cable (as per this guide) should not affect touch ID. Just be careful around that home button.

There is not much feed back yet for iPhone 6 repair and trouble-shooting, but replacing the cable could be a good place to start if you think that you tore it somehow during the screen replacement.

Before replacing anything, you can try hard-rebooting or power cycling your iPhone (to power-cycle, disconnect then reconnect your battery, then connect to WiFi to reset date and time).