Does kinetic friction always oppose the direction of motion?

No it does not. In some cases friction can cause motion. To illustrate this we will consider a body M₁ of length L placed on a frictionless surface and a smaller body M₂ placed on top of M₁ on the leftmost edge of it. The coefficient of kinetic friction between M₁ and M₂  is μ_k and the positive direction of motion is to the right. If we start applying a force F on M₂ of big enough magnitude, it will start moving on top of M₁ towards the rightmost edge of it. The forces acting on M₁ on the x-axis will be the positive force F we are applying and a negative frictional force F_F12 applied on M₂ by M_1.. According to Newton's Third Law, there must be an opposite - equal in magnitude and opposite in direction - force acting on M₁ by M₂, ie the reaction of F_F12. This positive frictional force, F_F21, is the only force acting on M₁ on the x-axis, and therefore causes it to move towards the right.