Is there a way to randomize files being sent over to a flash drive?

Need more detail to understand your particular scenario and desired goal. Some questions to start:

1. What device / system / software will be playing the MP3 files from the flash drive?
2. What is the total size of your audio file collection?
3. What is the capacity size of your flash drive?
4. Are all the music files in the same MP3 file format? Other formats such as M4A, MP4, OGG, FLAC, etc.

It may not be necessary to randomly copy files to the flash drive providing the flash drive is large enough to hold the entire collection. You can get a 512GB flash drive for approximately $50 USD. Most players software or hardware have a shuffle feature which would give you a random playback. [WARNING: look at name brands such as Sandisk, PNY, etc. if the cost of their drives are wildly more expensive than some no-name Chinese knockoff where a 2TB flash drive is selling for a mere $20 then that is too good to be true and it is a scam]

Not sure what you mean by corrupted files or unlikely to play files. Please elaborate.

So according to the Amazon Q&A the MP3 built-in player doesn't support playlists nor does it have a shuffle mode and it appears to play files either in the physical order they are written to disk which is not how Finder will display them. Also it seems to use the artist ID3 tag and will group files for playback based on the artist ID3 tag. You might be able to edit the artist ID3 tag within the MP3 file so as to ensure the files play in a somewhat random order of your choosing.

But honestly, the built-in MP3 player is quite unsophisticated to the extreme.

The radio does have bluetooth have you tried sending a playlist from the iMac to the radio treating it like a dumb bluetooth speaker? Thus using the iMac to control the shuffle, etc.