Transcribe is a web application and so can be used on multiple devices, as long you're using a supported browser.
A single user license can be used to access the app on multiple computers / devices, as long as it's the same individual using it on all these devices. You just need to login with the same email and password that you purchased the license under.
One thing to note is that transcripts that are typed/edited on a particular device are only available on that device and are not synced across devices. This is a specific privacy feature we built where the text you type is only stored in the browser you typed it on and is not sent to our servers. If you would still like the transcript to be available on multiple devices, you want to export the transcript from Transcribe and store it on something like Dropbox / GoogleDrive / OneDrive to have it sync between devices.