Stapro do a good flame retardant, if used correctly it leaves no trace that you can see or feel.
As said above, "dry clean only" is often used to cover the butts of the manufacturers and retailers - you need to test and draw your own conclusions. In the last few years, I can only think of one suite I've elected to dry clean as a "safe" option, but even then it was mostly because it didn't look dirty in the slightest.
Back down your pressure/flow rate a bit and make sure you get it well on the way to being dry before you leave.