it's obviously not instant, can it be very fast- sure
the amount of time it takes to warp things is very short, lets examin his susanoo arrow feat.
The kamui works by looking at a point and warping whatever is their, it should be noted that Kamui doesnot follow/move to its target. so, in order to warp the kamui arrows, it has to atleast warp fast enough to hit the arrows before they left kamui's area of effect.
So yes, if you are hit by kamui, you would have to be extermly fast to leave its area of affect before being warped.- Nobody has a feat of going fast enough to do that, so for the purposes of a verses match, if kakashi hits you with kamui you are getting warped.
So yes, kamui isnot instant, but it is fast enough to be considered so because no character in the manga is remoty fast enough to move that fast. I would argue that at max speed it might be faster than light ( black whole) because Obito thought he could warp Minato and he could teleport. Also, kamui hit the gedou right as it was being summoned.
Is kamui faster than amaterasu? nope- it has not shown to be faster at all.- I think people need to realize that being faster than a person can see doesnot mean you are faster than the attack. I can run circles around you on a bike, and you won't be able to aim and hit with a gun, but I am still slower than a bullet.
-Once ammaterasu is prepped it is instant for a certain distance after that it flies in the air at a much slower rate. sasuke shows that once ammy is active, it instantly appears all the way up to probably about 15 feet away.
We know kamui teleports at different speeds according to the user, however using feats, we cannot say that it can be amped up to instantaneous, mabey ftl but not instant.
Note: I am not saying that you have to be FTL to dodge kamui from kakashi, lol not at all. It takes prep to activate kamui and then kakashi has to aim as well. What I am saying is that if you are fast enough, even if kakashi activated kamui and it hits you-you might be able to get away.
-Amaterasu is faster because even if you are FTL +, if are are within its spawning range ( it doesnot come from sasuke's eyes, it spontainiasly appears were he is looking for a max of x distance- it would hit you. If sasuke activated ammy, and you are within range, no amount of speed is going to allow you to avoid ammy. that doesnot apply to kamui because it doesnot have the feats to support that notion.
Note: if you cite that Minato teleported away from obito, recall that obito was only like 14 and he said he could have warped even faster.