Add brown sugar at flameout. Anything over 160F will pastuerize/sterilize the sugar, and you DO NOT want to add sugars during the boil with the burner on, because you WILL burn it and caramelize some of it unless you stir like a maniac, which again is not advised with a boil going. There's a reason you never add DME/LME with the burner on, and sugar falls into the same category.
There are ZERO advantages to adding sugar to the boil and alot that can go wrong, so just add brown sugar at flameout and stir it in until completely dissolved!!