Add the film burn clip to a track above your clips and then add the Blend effect from Mixes in the Effects panel to the film burn clip. Now change the method to Add or Screen and it should look like you want. In my test, I keyframed the opacity so that it started and ended at 0%, while in the middle it was eased like a rainbow to 100%. This makes the effect appear more gradually. The default was a little too harsh for me. It's up to you though!

Thanks for the help! I got the film burn to overlay with Blend effect nicely.

Keyframing was definitely a great idea. oscillating from 0-85% for me makes the film burn look a lot smoother in relation to my main footage.

Thanks for all your help rhinox and everyone else too. Happy editing!