Can coefficient of kinetic friction be same as coefficient of static friction? I know coefficient of kinetic friction can't be greater than coefficient of static friction. But can they be the same? If so at what condition?
 A: As with many problems in physics, the start of understanding is getting the right kind of metaphor and the right level of abstraction.
What is happening when two materials are in contact?
At the level of rough surfaces, in the range of "many" atoms (many thousands up) the contact consists of little parts of one surface poking down past the up-poking bits of the ther surface. In order to move the two surfaces have to separate slightly so the poky-bits can pass by eachother. Unless a few of them break off, such as you get from abrasion.  So it can be thought of as little hooks that can catch on to the other surface. You have to pull these away before the surfaces can start to slide.
At a smaller level, in the range of "few" atoms (some tens or so) there are various low energy bonds that can form.  It is not typically forming new molecules. It's just that there are places on the molecules of one substance such that they attract the molecules of the other. Rubber and similar products have very large and complicated molecular structures. Often even very highly diverse molecular structures, almost haphazard. This provides huge opportunity for the molecules of the other side to find places that are slightly lower energy when they are close together. These act as a huge number of much smaller hooks.
Thse effects can be significantly increased if one of the surfaces can deform a bit so as to conform to the other very tightly. This is part of how such things as rubber tires manage to grip the road.
When the two surfaces are sliding these various hooks have less chance to find good purchase.
This indicates when you should expect to find the surfaces have little difference between static and kinetic friction. The surfaces should be rigid to reduce deformation. They should have very little surface roughness. The molecules should not have readily available interaction sites for the other surface to latch onto.
And @Bob D has given us a link. Thanks Bob!  There we find polytetrafluoroethylene otherwise known as teflon. It has 0.04 for both static and kinetic. This is also a non-stick coating used in cookware. The basic idea is that it seriously reduces both the mechanical and molecular "hooks" holding one surface to the other. This tends to make friction low for both, while reducing the difference.
