Brown is NOT all that bad, black would be bad, but brown is an indication that service is needed immediately, but it does not mean impending doom for the transmission.
I do not agree with flushing transmissions, I think it is a waste of money, and if not done correctly, can do more damage than good. Do have the transmission fluid changed and teh filter replaced/cleaned. This means the pan has to be dropped.
When you have this service done, make sure the mechanic uses only the specified fluid for your transmission. Your owners manual will tell you what is required.
Flush vs drain and fill.
In a drain and fill, the fluid is drained and fresh fluid is put back in, much like an oil change. With automatic transmissions only about 40-60% can be drained at any one time, so a lot of the oil fluid remains. If you follow the manufacturers recommended change interval, the fluid will always be good enough for the life of the vehicle. You can do back to back fluid changes every 5-10k miles to catch up if needed.
A flush involves disconnecting a cooling line and letting the transmission pump the old fluid into a waste container. the transmission is refilled by a machine through the port where the cooling line was disconnected at the same rate the old fluid is pumped out. In theory, this should be better. The fluid is sucked out of one end of the oil pan and filled from the other.
Old fluid is constantly being mixed with fresh fluid so it isn’t as efficient as it appears to be. It costs more because it needs a lot more new fluid because of the amount of new that gets sucked out with the old, and the machine costs money that the mechanic would like to recover. In many cases, the mechanic doesn’t drop the pan to clean out the sludge or replace/clean the filter.
Get good estimates from reputable shops and make the decision that you think is best for you.