Well I had a rattle I couldn't figure out until someone on here posted a thread about it. Not sure if your rattle is it, hard to tell from the video, but there is a thin piece of dark grey fabric (I think it is a splash guard) in the driver wheel well that has the letters AE cut out on the bottom of it that is attached with 4 plastic pins. The very top one by my UCA was the culprit. As a quick check I just sprayed some WD40 on it. Stopped the squeak immediately. Permanent fix is to find some two sided foam tape and put it between the metal and the piece of fabric and then run the pin through it to secure it so it won't move. Never would have figured it out had it not been for a topic on this forum.

I just re-checked your post and you said mud-flaps in your wheel well so that may be the same thing I am talking about. I thought you might have mean the mud-flaps that prevents mud from slinging up on the side of the truck.