I don’t use Premiere, but if the blend modes are anything like all other Adobe products, then it should be as follows…
If you want to keep the dark bits and lose the light bits (as in the example you showed) then use Multiply.
If you want to keep the light bits and lose the dark bits, then use Screen. (You can also use add and this adds the layers together - the effect is similar but more glowy)
If you have something that’s against a mid greyish background and you want to keep both light and dark bits, then you could try Hard Light or Pin Light.
I’d be surprised if Premiere couldn’t pick up an alpha channel, so if the image doesn’t have an alpha, you can make one in AE.
Method 1: Import footage into AE. Make a black layer, put your film damage footage above it. Set the matte channel of the black layer to luma inverted matte.
Method 2: Import your footage into AE. Apply an invert effect. (Channel -> Invert). Apply a Set Channels effect (Channel -> Set Channels) and set it as follows… Red to Source: Off, Green to Source: Off, Blue to Source: Off, Alpha to Source: Luminance.
Hey presto! One alpha channel. Infact, I use this luminance to alpha technique so often (method 2) that it must be my number 1 effect preset.
Hope that’s useful.