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I actually contacted Toshiba, who said that it was possible, and then transferred me to amazon, where the agent was unable to provide instructions. It seems neither Toshiba nor Amazon know the answer, despite it being an advertised feature. Thanks for the reply.
I have the 43" 4K version of the Toshiba Fire TV. I got my flash drive to work with the tv by going into Settings -> Device & Software -> USB Drive -> Format to Internal Storage.
Make sure you're using either a empty flash drive, or one with files you don't mind being deleted. Selecting the above option formats/erases any files on the drive. In my case I bought a 32GB Sandisk drive to use with the TV and it seems to be working fine. I don't pause live TV for a long time though, only about 3-5 minutes to go get a drink, food, etc. Note too that pausing on a channel won't save the recording if you switch channels. And you can only rewind to when you first started watching a channel. That has been my experience anyway with how the rewind/pause/fast forward works.
It didn't work for me. I did what you said formatted to internal memory and still limited to 2 min rewind? I've searched the manual, forums, etc just as the OP did to no help. Any Amazon support would be nice!?
Ok, figured it out. Sadly this is not in the manual (actually the manual is crap). You have to first format your flash drive to fat32 via windows PC (this step is needed if the tv doesn't recognize the USB drive as sometimes it will detect the drive and ask to format automatically, BUT NOT ALWAYS) so that the fire TV or stick will recognize the USB. Then put it into the tv and go-to the settings, device & software, USB drive and choose the "format to internal storage" option. Then once that is done undo it by going to the same settings place and choosing to return the drive to external storage via "format to external storage". Then all of a sudden it will begin to work with the live TV function (did for me anyway). I had it set to external to begin with but I'm guessing something in the formatting makes it work. The drive originally asked me to format on first plugin but for some reason that didn't work. So now you have the answer! Don't bother calling Insignia or Amazon as neither know what is what. Also my tv is the Insignia Fire TV Edition model NS-55DF710NA19 (55inch 4K HDR).