The question could boil down to IMHO:
Can I reuse copyrighted media in some FOSS software?
The key point is to determine whether or not you are authorized in general to do so.
I assume you mean that this app is likely open source itself but it does not matter much. The format of the media does not matter either (it could be a Gif, mp4 or else). And in fact it could be an Android app or anything else: Android does not matter here. And the fact the app is distributed on some app store does not matter too: Google is unlikely to allow unauthorized redistribution in any case but what matters is whether you are authorized in general irrespective of Google.
So if the copyrighted material has some explicit FOSS license that allows redistribution, then yes. This is quite unlikely for a TV series like Friends.
But if this is a small excerpt that could be considered "fair use" it may be acceptable in some cases. That determination is not really easy and may not be valid in all countries. I would shy away to claim fair use unless I get real legal advice on that very specific case.
Otherwise, the answer is a clear NO unless you get permissions to do so. Here, this would require some kind of commercial licensing deal with the owner of the Friends TV series. Good luck!