Hi IrnBruMuffin,
By 'loaded locally into the app' do you mean uploaded as part of the app Media Library?
If that's the case, then my experience on the mobile app is slightly different to a browser - the mobile app will download the App package and all media library images the first time the app is loaded and they then seem to be available to the app fairly quickly after that - future app loads just launch the app and the images are immediately available in the app cache.
This is largely because the app cache can be made persistent on a mobile device inside the PowerApps 'container', whereas the app player through the browser renders the app 'online'. That online space must load the app and it's images every time the app is run, so if you have large images, or your internet link is sometimes a littly slow, you will get a different experience. Images seem to be loaded only when they're are used on a screen when using the web player.
I haven't tested this, but you can try placing images onto the loading screen and hiding them - this may force the player and/or browser to load them into cache which might speed up loading when you actually display them later.
If you're accessing the images from a source (like OneDrive or SharePoint) then the best way to deal with loading delays is to load them into a collection on startup and then reference the collection in later screens.
Eg: I often use Office365Users photo images, but because our data is a few continents away there is always a lag when loading them. The first thing I do is collect all the images I need on screen one, after that I reference them in the collection instead of calling Office365users again later.
As always, when using custom uploaded images, ensure you always optimise them beforehand - use a photo editor to reduce size, colour depth and see what format you're saving them as.
Hope this helps,
RT
