I personally don't think its a good idea to do the flush while you travel. When I had to travel, I decided to do the apple fast while on the move and did the flush as soon as i got back home on the third day- and that was a great flush- got the kind of stuff out that i did not get wihtout the apple fast the first time around. but that just my experience.
You sure could do it while on your period but it just could leave you completely exhausted- i would not do it if i were on my third day and aslo traveling- if I were home -I might have done it! Wonder if this helps at all....?