I actually was using .zip files someone had linked to elsewhere here on AtariAge. I also tried .ctg versions, but RetroArch doesn't see them at all. Can you suggest a safe link to obtain the .rpk versions?
With the .zip versions, RetroArch acts like it's loading but doesn't get to the TI994a start screen at all -- just a grayish blank screen with the MAME controls below it.
The RetroArch interface on Kindle Fire is pretty easy/obvious for other systems. I just tap "load content", navigate to the ROM folder, swipe down and tap the ROM I want, then sometimes select from among a few different cores (presumably because RetroArch thinks more than one might run the ROM), and then the thing runs. Some run slow, but the TI99 games are the only ones that don't run at all. I use an iPega controller connected wired via USB-C, and it makes for a really convenient portable system.