They are text subtitles, SRT/SSA/ASS, correct? Plex does not support external image based subtitles such as PGS or VOBSUB.
There is an external subtitle fix in the 9.1 client beta (see first announcement below). Unknown when 9.1 will go from beta to mainstream. You can subscribe to the mainstream release announcement (2nd thread below) to receive notifications of updates (scroll to bottom of thread, change Normal to Watching).
If desired, you can sideload the beta release. Use the Amazon Fire OS Devices version. Sideloaded apps do not update via the Amazon store. To return to mainstream releases, delete the sideloaded version and install the Amazon store version.
