The pen is a DIY silver pen.
From this I am assuming you are not using using any kit parts, but are making the parts and tapping the threads yourself.
If so, and you already have the flat facets on the outside and can't put them on after the threading is done, just cut your threads. Now you just have to take a little bit off the end of the cap where it contacts the pen body to make the flats line up, little by little creep up on the perfect fit.
It might just take a wipe on 400 grit sandpaper each time to see it getting closer to lining up, depending on how hard your material is.