Obito: Near instant.
Kakashi: Can be close to Obito's, seems size dependant.
If I were to make an educated guess, I'd say it takes between 0.3 and 0.8 seconds overall. A fast Kamui from Obito was countered by FTG initiated by Minato, his reaction times aren't spectacular so I'd say it took around 0.3 seconds for him to react and 0.05 seconds extra to initiate the teleportation.
Kakashi reacted to, and warped a Susano'o arrow which can cover a small distance quite quickly - taking into account that the size of the Kamui wouldn't need to be large and that Danzo had enough time to let the Senju DNA manifest into a tree whilst the arrow was mid-transit, you could say Kakashi managed to Kamui it in around 0.8 seconds.