I personally use a free file manager from the Appstore. Search "File Manager" on the Appstore and you'll most likely see a yellow-ish folder icon, which is the one I use
Once you download the textures, go into the launcher settings, tap on the textures tab on the top, press select, and go into your download folder. Find the pack you downloaded, and tap it. This does not require any unzipping of the fileIf the textures don't work, that's a bug with the pack, not the launcher
how do you unzip file on kindle fire?