I spoke with my father in-law, who has been an appliance repair
technician for more than 50 years.
He says using pipe dope on the flared fitting is fine, as long as you
follow a couple simple rules:
1) Use the proper pipe dope. What you want is called "stick pipe
dope" (ask at your favorite hardware store), and is meant specifically
for natural gas connections. DO NOT use plumbing pipe dope, which is
typically oil based - it can get into the gas line and foul the line,
necessitating a replacement. You don't want to deal with that.
2) Be certain to avoid the top two or three threads when applying the
pipe dope. This is to ensure that nothing gets into the line.
3) Apply the pipe dope sparingly. (again, to make sure nothing gets
into the line).
You can do without the pipe dope if it makes you nervous, but should
you find later that you want a new dryer, getting the line
disconnected could be a problem if corrosion has set in and the
threads are "un-doped".
Hope this helps!
Source: experienced appliance repair technician