I'm about 5'10" and 200 lbs. I wear medium shirts but the cotton ones always shrink in the wash. Then they fit like a small. Does this shirt shrink?

No. BUT, I take great care with my laundry. I wash in normal, WARM water. Good detergent, Tide Free. I have a front loader.. I dry on a low heat, casual cycle, only long enough to get the wrinkles out. Hang to finish drying. I iron with Magic Spray Sizing to give it a crisp body. If you don't want to iron, throw in a dryer sheet but take out when wrinkles a re e gone and hang. It really is,well made and if you want to dry it longer it will still be ok. It's not a cheap shirt. Don't treat it like one. My husband has had one for 8 years and it still looks new.

Are these shirts so long that you have to tuck them into your pants? Are they roomy enough to not have a concealed handgun noticeable?

They do need to be tucked into your pants, but they are roomy enough to carry concealed. Although, I have not carried concealed with them, it appears it would need to be a smaller light weight weapon to keep from printing. You know showing the form of the weapons shape in the fabric.

I'm 6'1, 175lb, 40 chest what size should i buy? Thanks

I'm 6'4 50 chest 250lbs.... I get a XXL because I use this wonderful shirt as a light jacket. If I need to layer, a hoodie fits nicely under the shirt. Not much use to what you are asking I know... Large might be the size you need.... you can send it back if fit is incorrect.