The instructions for copying the firmware for the BTD500 are incorrect for standard Linux (the kernel.org version). The firmwares for a USB adapter are named “rtl8671bu_fw.bin” and rtl8671bu_config.bin. The names given in the Kinivo app note are for a UART connected version, not the Kinivo product. The Kinivo firmware works fine, when properly renamed. I suggest keeping the original names and symlinking to them, since the github kernel-firmware tarball will clobber the Kinivo firmware until it gets included there (if it does).
Although the BTD400 adapter (which I also have) is not formally supported on Linux, it also works fine after adding firmware, in this case brcm/BCM20702A1-0a5c-21e8.hcd from winterheart on github, The BTD400 uses a Broadcom chip (obviously). Kinivo might consider adding an app note for that… The Broadcom files in the kernel-firmware tarball have very fussy names and the ones there are not picked up by the Linux Broadcom bluetooth code
