This is a great question that I wished went a bit further. In this scenario I voted for Amir to start, but I think changes are needed to stabilize our 2nd unit... which would involve moving a few of our current starters to the 2nd unit.
Starting Lineup: Horford, Amir, Brown, Bradley, IT (Good ball movement and decision making, with big shot potential and slashing with Brown and IT)
2nd Unit: KO, JJ, Crowder, Green, Smart (Defensive grit, floor-spacing bigs that can clear out creating room for Green to slash... heavy Smart post-ups)
In the playoffs you're not going to run a full second unit without any starters. I like the idea of Brown starting over Bradley, especially against teams with big scoring twos like Derozan. Then bring Bradley and KO off the bench first for Horford and Brown (KO, Amir, Crowder, Bradley, Thomas), followed by Smart (KO, Amir, Crowder, Bradley, Smart). Then start mixing Horford and Brown back in (Horford, KO,Brown, Bradley, Smart), along with JJ, Rozier or Zeller as matchups dictate.