[stumped]

sure, you can convert any unlocked books to kindle format and sideload, or get them there, as mobi, using the send via email to kindle feature

the way it works for several of the epub reader apps: moon+ , bookari... amazon app store sell versions, but they flag them as not compatible with fire tablets ( they are really, but amazon want you to use their solutions, so any reader app that can do text to speech is flagged as incompatible)

that means that - from a fire tablet- you do not see them as apps that you can buy.
you can however buy them using the amazon app store app on an android tablet or using an android emulator on PC. Then you have to figure how to move the purchased app to a fire tablet that is registered to the same amazon account, for it to work.
the other workaround is that you add all the google services to fire tablet then buy your reader apps from google play store. that way you get the latest greatest apps, but that method only works for more recent fire tablets - you can add google store to tablets running fire os 5, and probably to any running os 6...
i used to have a 2nd gen kindle fire for grandson and was able to buy and install the ALDIKO epub reader app, that may still be the case. go to apps on the tablet and see if it is available. there may be a free trial/demo/stripped down version also
NB with reader apps that are in both app stores - google and amazon - the amazon version is often older and slow to update
android tablets( not from amazon) CAN RUN A KINDLE FOR ANDROID APP if you dont want to have to convert your amazon books. ipads also have an app but you cannot buy amazon books directly from apple devices because amazon do not want to pay the 30% apple commision

IMHO the simplest solution is to put all the books you buy , from whoever, into calibre - de-drming them as you go, then you can sideload anything to anything from calibre. there are threads about how to do that, using old versions of Kindle for PC for the amazon books