With the off day Thursday and next Monday, I think they can reasonably skip Brown's next start or two:
5/26 (COL) Taillon
5/27 (COL) Horton
5/28 (COL) Boyd
5/29 OFF
5/30 (CIN) Rea
5/31 (CIN) Taillon
6/1 (CIN) Horton
6/2 OFF
6/3 (@WSH) Boyd
6/4 (@WSH) Rea
6/5 (@WSH) Taillon
No days off from 6/3 to 6/15, so you'd need a 5th starter in that stretch