Hello unclegally,
If your iLok licences are currently activated to iLok Cloud then that's fine -- you can use iLok Cloud from any computer. On your new Windows installation, you should just need to make sure that iLok License Manager is installed (which can be downloaded here if needed: https://ilok.com/#!home ), then within iLok License Manager use 'File | Close All Cloud Sessions' if it isn't greyed out, then use 'File | Open Your Cloud Session'.
I.e. you can only have an iLok Cloud session open on one computer/system at a time, and you need to have one open on whichever computer/system that you want to use at the time.