This combination is best against guys who have good, in-guard posture. It's one of the many gems in Kid Peligro's book, The Essential Guard.
Start with the kimura attack (actually, you could start anywhere in the rotation). If he leans in the direction of the kimura in an attempt to counter, then follow-up with the cross-over sweep.
If he postures forward, ducking his head to counter the cross-over sweep (essentially, he would be breaking his own good posture), then go for the guillotine attack--or the modified "front naked choke" that Rodrigo showed us as an alternative. Same choking position with the one arm, but instead of grabbing the hand of that arm and pulling up, you hook that hand with your other arm and put the forearm of that other arm behind the guy's head/neck.
If he tries to posture up from the guillotine attack--especially if he plants his hand on the mat in an attempt to "push up" and relieve the pressure of the choke, then go back to the beginning with the kimura attack on the arm that is posting up.
The order can be switched around depending on the guy's reaction. For example, when I slapped a kimura on Maggie the other day, she countered by ducking her head, lowering her posture and grabbing her own gi. Here, it makes more sense to follow-up with a guillotine attack rather than the cross-over sweep. Why? Because her lower posture would make the cross-over sweep much, much harder to pull off.
(A side note: it wasn't a kimura attack from the closed guard. I was in more of an open/butterfly guard. But I think the principle is more or less the same.)
