Why not just buy a YN622 radio transceiver, set it to receive, and attach it to the Amazon Basic flash's hot foot?
(Since the YN685 has an internal YN622 receiver, I'm assuming you are using a YN622C or YN622C-TX to trigger it. The YN685 also can be set to receive manual only signals from a YN560-TX/RF603/RF605 transmitter. If you are triggering the YN685 with a YN560-TX or RF/603/RF605 transmitter, you could use either a YN622C made after December 2014 set to YN560 receive mode or use an RF603 or RF605 to trigger the Amazon Basics flash.)
The Amazon Basic flash's power will still need to be controlled manually via the flash's own control panel, but the YN622 will trigger the flash to fire in sync with the camera. YN622 transceivers also have a PC port that would allow you to trigger it via a PC cable between the YN622 and the Amazon Basics flash.
Both the Yongnuo and the Amazon flash have PC slots, so I don't know if I can connect a PC cable from one flash to the other and fire the Yngnuo with the trigger.
The PC port on the YN685 is a "receive" only port. It does not "send" a signal when the YN685 is triggered via wireless or the hot foot. After playing around with a YN568EX II, YN685, and YN622C triggers I can conform that to be the case. When I trigger the YN685 via a YN622C-TX it does not trigger a YN568EX II connected to the YN685 via a PC cord. When the same cord is connected directly to the YN622C-TX (or a YN622C), it does fire the YN568EX II.