Well Brad Stevens has been here for 3 years, and this is a quick breakdown of the players who haves started.
2014: 12 of 19 players started. All 9 players who averaged 20+mpg started, 11 of the 13 players who averaged 15+ mpg started, 9 of 10 players who played 40 or more games started. Only Green and Rondo started every game they played.
2015: 12 of 22 players started. 11 of the 13 players who averaged 20+mpg started (there were 2 players who avg 15-20mpg, neither started). 8 of the 9 players who played more than 40 games started. Only Bradley, Green, and Rondo started every game they played.
2016: 10 of 16 players started. 8 of 8 who played 20+mpg started, 9 of the 10 players who averaged 15+ mpg started, same for those who played 40+ games (Jerebko being the lone regular to never start). Only Crowder started every game he played.
Obviously the C's had a few trades and injuries each year, but I'd also be surprised if there weren't any trades or injuries this year. If you're a regular rotation player with Stevens, it looks like you'll get your chance to start multiple games, and I think that trend will continue this year and Brown will get to start a handful of games.
Worst case, hopefully the C's have the their playoff seed firmly locked up this year at the end of the season, and he'll get to start the last game of the season on 4/12 when Stevens rolls out the Celticsblog dream lineup of Rozier, Jackson, Hunter, Brown, Mickey.