They work as a team and take turns to deal with customers and then split their profits at the end.
They work as a group and take turns to handle customers and then divide their profits at the end.
彼らはチーム制で働く ＝ they work as a team; they work as a group
順番に ＝ take turns to; in order
客を捌き = deal with customers; handle customers
最後に = at the end
利益を分配する = split their profits; divide their profits
利益 = profit
アメリカ合衆国 
