I sprayed my flash tube lightly with black paint and just rubbed at it with 0000 steel wool. It shouldn't be overdone, unless you're going for a different look. I've seen some people paint the tip and and work their way back to chrome, but I did mine like the reference shows: chrome tip back to some weathering.
I just finished weathering my Dankenman sidearm tonight using wash of Tamiya Flat Black acryllic that I applied quite liberally and then wiped away with a tissue. I let some areas dry longer to give that carbon-scored look. I then added a very thin wash of Tamiya Flat Brown to give the hint of rust/oil before lightly sanding with 120 and 1000 grit sandpaper. I know you asked about the EE-3 and not the sidearm, but I plan on doing something similar (or maybe not quite so heavily weathered) with the EE-3. This is one of Dankenman's "seconds" so I intentionally went a little heavy with the weathering; I'm planning on being a lot easier on my Mojo (the grip of which is visible in the top of the frame) when I get to it. I highly recommend both, BTW.