When it comes to cotton flannel shirts, the choice of dry clean vs. launder comes down to a question of personal preference.....an ultra soft feel or a slightly soft feel to the fabric. As a consumer, the choice is yours to make.
Here's a brief guide to making the right choice for yourself:
Cleaners, typically, handle cotton flannel shirts in one of two ways:
1. Launder, toss in a dryer and press (hopefully by hand, not machine). Water based stains (perspiration, beer, coffee, juice, etc.) are removed but oil based stains (body oils, creams, lotions, salad dressing, etc.) will most likely remain. Result in feel or "hand": PASSABLE
2. Rinse or wetclean (to remove water based stains), hang dry, dry clean (to remove oil based stains) and press (hopefully by hand, not machine). Result in feel or "hand": ULTRA SOFT.
As regards point 2 above, I would prefer dry cleaning in siloxane (used by a about 5% of cleaners), not perc or synthetic petroleum (used by about 95% of cleaners).
If that cotton flannel shirt was mine and I was given the choice of dry cleaning in perc or synthetic petroleum vs launder, I'd probably ask the cleaner to just dry clean (not press), return it to me and take it home to launder, toss in a dryer on low and hand iron myself. If I was given the choice of wetclean, hang dry, dry clean in siloxane and hand iron, I'd choose the latter.
As I said before, it's a matter of personal preference. And the answer is a little more complicated than what you might have previously surmised.