Hi @3m,
Well Currently I don't think that is possible.
The URL you used seems to be related with the OWA service, which I think it would need authentication first before it could get information from server side. Would you please share more details for that?
In PowerApps, the URL is somehow hardcoded within the Image control, currently there is no way available to change its value (I mean the parameter used for the URL, such as user specific information).
For your situation, I think the URL works under Chrome should be that you have OWA sessions connected.For Mobile or Internet Explorer 11, what is the error message showing out under the image control?
For now, PowerApps has Office 365 User and Office 365 Outlook added as available connection, which makes it available to get some of the user or email information, but there is no image attribute supported yet.
You may consider submit an idea to suggest Office 365 User connection add the image attribute support.
Regards