Would Album Art in an app screenshot be protected by Fair Use?
Your best bet would be to contact several bands and ask for written permission to use their art in your promotion.
My expectation on reading all the terms of service of many music streaming services is that they do not grant a commercial license to any of the content they provide, so you would be scraping that content against the terms of service. To my reading this is explicitly prohibited by SoundCloud:

(ii) You must not adapt, copy, republish, make available or otherwise communicate to the public, display, perform, transfer, share, distribute or otherwise use or exploit any Content on or from the Platform, except (i) where such Content is Your Content, or (ii) as permitted under these Terms of Use, and within the parameters set by the Uploader (for example, under the terms of Creative Commons licences selected by the Uploader).
(iii) You must not use any Content (other than Your Content) in any way that is designed to create a separate content service or that replicates any part of the Platform offering.

That alone should land you in hot water with Apple's review team.
If I were submitting an app, I would be forthright and proactive about mentioning that the artwork submitted is authorized in writing by the owners and/or properly licensed. SoundCloud also makes note that you can re-use your owned content or content that you have a license to use (uploaded content with CreativeCommons that is permissive enough for commercial reuse should do the trick if you don't have a more specific license)
If you can't do that, pay an artist to make a fake album cover - perhaps mixing elements you like and paying that artist for the rights to their work. You can upload content to soundcloud quite easily so you could control that image in a manner that Apple could rapidly determine that your company was in fact the original rights holder to the content chosen for the full screen image if not for all of the smaller thumbnails.
Fair Use is only of use in the US as a defense if you are sued in court. Expecting it to get you past Apple's policies seems like an uphill battle as you don't have a right to dispute their policies and they are fairly clear that 3.1 of https://developer.apple.com/app-store/marketing/guidelines/#photography

Show only content you have the legal right to display.

There is some precedent that thumbnail images are allowable under fair use doctrine by internet search engines, but that's a far stretch from you selecting one static image for promoting your work on a third party app store.
Your defense might be you are in fact &quot;Display the app on an Apple product exactly as a customer will experience it when the app is running.&quot; but you run the risk of Apple asking you for confirmation that you have licensed that content - either from SoundCloud or the holder of the copyright on the album cover you choose for self-promotion.