I'm assuming your data source is an excel spreadsheet?
By default, data isn't stored in the app. The app is just surfacing data for users from a data source. But you can store data in the app with collections
A bit of context about collections (i.e. storing data in the local app):
To store data in the app itself, you can use collections. Collections are basically tables that allow you to store data locally (i.e. in the user's local browser where they have the app open) - and you can store images in collections. However, when you add data from a data source to a Power App collection, it does so in the user/authentication context of the user interacting with the app - which means if they don't have access to the images, they won't be added to the collection.
In your scenario, however, you probably don't need to use a collection. Just thought I'd give a little context.
I'd say your best bet (if you haven't already done so) is to copy all the images to a location in SharePoint Online that's accessible to end users, then change the URLs of the images in the spreadsheet to be this new location. So long as users have read access to the images in SharePoint, they should render just fine in the app for users.
