In The Flash episode "Legends of Today" (Season 2, Episode 8), Team Arrow is not doing well in their fight with Damien Darhk and his Ghosts when Barry Allen comes in and speeds them out. Damien Darhk is quite surprised by this development, and didn't seem to have any way to react to Flash.
Why doesn't Arrow just ask Flash to capture Damien Darhk? Sure, they may not understand his magic, but surely Flash could speed in, inject him with a tranquilizer, and then carry his unconscious body to Oliver and the team. (Heck, he could even give John Constantine a call and ask him to put a binding spell or something on Darhk before he wakes up).
So why doesn't Arrow just ask Flash to capture Damien Darhk?
And yes, I'm fully aware that the out-of-universe reason is that there wouldn't be a villain for Season 4 if this happened.