What steps should I take after kitty litter has been washed down the drain?
If it rinsed down the drain and hasn't clogged yet then you're in fairly good shape.  Clumping litter definitely can be saturated and breaks down.  I'm assuming this is some sort of clay based litter (I use a pine based product myself) with fairly small granules and not a lot of stone.

Also I'm presuming that you haven't been flushing the line out with water continuously, and so if any clumping was going to occur, it would have.

If you have access to any of the traps I would go ahead and put a bucket underneath and open them up just to be certain.

If you don't have access then you either continue to flush the line or you could use a plumber's snake (a home version is a great investment) to disturb any settled litter possibly while flushing.

Not a magic bullet, but probably a measured response.