Is 1/2" flexible gas pipe adequate for a 22000 BTU clothes dryer?
I concur, 1/2 inch gas pipe is adequate for the dryer. The only thing I would like to add Is, did the gas company run a 2 psi meter to your home? 
 an easy way to tell is if there is a gas regulator at each appliance. This is a pretty common practice in the state I live in. If it is a 2lbs system, you'll need to have a regulator added to the new appliance. Just something to be aware of.