Is it OK, patent-wise, to use FFMPEG (for transcoding and video trimming) in a commercial application, be it free of charge or pay per install, on Android and iOS considering that both Google and Apple already pay royalties to MPEGLA?
The fact that Apple or Google pay royalties to MPEG-LA does not mean that you are covered and that you do not have to obtain a license yourself.
Patent-wise, irrespective of which software is used (be it open source or commercial) you may have to acquire a patent license and pay royalties for certain usages (for FFmpeg or any similar software).
Understanding which are these usages is a complicated matter...
Some things to consider:
what are the codecs used, and is this for encoding or decoding? In several cases, decoding may be OK, while encoding may require a patent license from MPEG-LA and/or other patent pools. In the case of FFmpeg, the configuration options determine which one can be used and can be verified by checking the "strings" of the built binaries objects/shared libraries. But as always with patents, using is what matters most afaik: building and not using a codec is different from using.
what is the type of usage? personal, free? or more commercial, enterprisey? Some codecs are OK to use for some personal non-commercial purpose, especially when only used for decoding.
So this is complicated, in some ways fubar. This is in all cases a long winding road to contact and obtain a license from these patent pools. Just figuring out which codec is patented and who to contact is already a complex task.
(as you may guess, I have been involved somewhat with this kind of things, good luck!)
There is an alternative which consist in buying commercial codecs that would bundle proper patent license(s). One company provides such a pack as far as I know but for use with GStreamer and not FFmpeg. In any case reading about their offering is interesting because you can learn about which codec is from which patent holder, something that is everything but self-evident.