How can I attach a silk flower to a pen?

Hot glue.

You cut the stem take out the cap in the end use glue of your choice put the stem in the cylinder, then cover the whole thing with floral tape. Any other questions?

They show you the technique in this project-http://www.hometalk.com/diy/decorate/rooms/add-some-romance-to-the-mundane-flower-pens-27113881

You can use a thick, green tape ( duct tape or floral tape) to make it look like a stem, have fun!!

If you have a really small space in end, so it fits well, use a 2 part epoxy. Put the stem in the cut off end, first dipping it into the 2 part epoxy. Epoxy is the strongest way of securing something in that small of a space.

I left the stem on and used green floral tape around the whole thing.

Without some sort of glue the floral tape will loose. It's only a wax glue activated by stretching the tape. With use and wiggling it will come loose.

I used them without glue for 2 years at the front lobby of a busy hospital and none of the floral tape came off.