What would be the appropriate time and duration to perform Kangaroo care (in which baby is supposed to make skin to skin contact) in order to increase breast milk?
If you're talking about what is officially termed "kangaroo care", for premature and special-needs babies, then you'd need to follow your doctors' recommendations for their care. Kangaroo care may be recommended for up to several hours at a time, but it would depend on how medically stable the baby was.
On the other hand, if you are talking about a more informal skin-to-skin contact for an otherwise healthy baby, for example if you are struggling with low supply issues, or even if you have plenty of supply but baby isn't gaining weight, then 48 hours of skin-to-skin time would almost certainly resolve it.
I literally took myself and the (then ~2 week old) baby off to bed for a whole weekend and got my husband to deliver regular snacks and drinks. We slept and snuggled and by the end of the weekend things were going much, much better.
There is a good summary of the research on skin-to-skin contact (including kangaroo care in premature and low birthweight babies) here: http://www.unicef.org.uk/BabyFriendly/News-and-Research/Research/Skin-to-skin-contact/