the problem with a firestick is that their isn't much space available to store recordings. for me I use nvidia shield with a portable hard drive connected to it, with tivimate.

not sure if the shield is an option for you budget wise.

I think you can get a cable that connects a hard drive to a firestick but don't know for sure

You can buy a OTG cable, that plugs into the power plug on the Fire TV stick, that gives you a plug for power and a USB A female plug, so you can add USB drive via it, check YouTube - there are a few video's about it. Just gave my Fire TV 4K stick to my Daughter, with such a cable, do do not have a photo. Sorry - my Shield Pro arrived to-day :)

If you have the 4k version, 2gen Cube or the latest release firestick and firestick lite than you can upgrade you storage space for recording throught tivimate also.

Use DUPLEXplay