Is it the same user?
Try to share the connection itself to the user.
Some connections must be shared.
We tested and Azure Blob Storage is one of those connectors that must be shared to the user.
- Go to make.powerapps.com
- Select Data
- Select Connections
- Look for your Connection, Azure Blob Storage
- Select Ellipses near Azure Blob Storage
- Select Share
- Share it with the Users who get that error
Also, try this:
Try clearing the Application Cache for "PowerApps" under Mobile Device Settings -> Applications (varied by device) and see if it reprompts you for the connection permissions from mobile device, especially after trying the above and/or trying to remove and recreate the connection.