I have traveled with my DE, but don't have a special kit. I took a tube of shaving cream, my DE razor, and my brush. I wrapped the brush and razor in a washcloth, and then tucked them in my regular kit. Worked fine. If you're really worried about it, take the blade out first. I didn't and didn't have trouble.
Brushes are tougher than they look, and as long as you don't leave them wrapped up, wet, for days they'll be fine. I dried it off with a towel so it was only a little damp, wrapped it up, and was good to go.
I haven't managed to shave on the train yet, although I noticed the restrooms have a slot for razor blades. I wonder how many they get these days.
I don't think I'd be brave enough to shave with the DE on a moving train.