Hi @NickGrant,
Do you want to share your On-premise Data Gateway with other users/your org within PowerApps?
Further, do you want to share the gateway to certain people/your Org to automatically get authorisation through their O365 account?
I have made a test on my side, if you want to share the gateway to certain people/your Org to automatically get authorization through their O365 account, I afraid that there is no way to achieve your needs in PowerApps currently.
If you would like this feature to be added in PowerApps, please submit an idea to PowerApps Ideas Forum:
https://powerusers.microsoft.com/t5/PowerApps-Ideas/idb-p/PowerAppsIdeas
When you shared the app (create a connection to File System using On-premise gateway) with other users, the On-premise Data Gateway would be also shared to them. But each user has to create their own File System connection on that Gateway when they run the app.
So when other users run the shared app, they would see a dialog to ask them to provide their own credential to File System:
Please check and see if the following thread would help in your scenario:
https://powerusers.microsoft.com/t5/General-Discussion/Gateway-Not-Shared/m-p/5813/highlight/true#M2632
Best regards,
Kris