Because /media is owned by root, plex will have issues.
Add the plex user to your group: sudo addgroup plex YOURGROUP
Then, open the “disks” app in ubuntu, choose your flash drive, click on the gear icon, click on Edit Mount Options, switch off auto mount, and then change the mount directory to something like “/mnt/myflashdrive”
You will see an entry like this in /etc/fstab:
/dev/disk/by-id/usb-JetFlash_Transcend_16GB_20LEYYIBYO01FB61-0:0-part1 /mnt/transcendflash auto nosuid,nodev,nofail,noauto,x-gvfs-show 0 0
If needed, restart plex.
All is good now