If a force is applied on a body in an isolated system, it gets accelerated, which means its velocity and hence its Kinetic Energy will go on increasing. How does law of conservation of energy holds for this increase in Kinetic Energy?
As you know, the Law of conservation of energy holds only for isolated systems. From Wikipedia,
Law of conservation of energy states that the total energy of an isolated system remains constant; it is said to be conserved over time.
Now, what is an isolated system in physics? As stated in Wikipedia, it is
a physical system so far removed from other systems that it does not interact with them.
You cannot apply a force on the body without interacting with it. So it is not possible for you, an external entity, to increase the kinetic energy of the isolated body, without breaking its isolation.
So you cannot apply energy conservation in this system. However, if you consider the system, including the body and the source of this force, energy conservation will hold.
Krishnanand J's answer gives a good explanation, however, I assume (by how you asked) that you are considering yourself to be a part of an isolated system. Now, if you are applying a force on the system, and the system is accelerating, then you are doing work on it. And you cannot do the work without using your energy. So the kinetic energy of the system which is increasing is due to the fact that chemical energy in your body is decreasing, and hence the total energy of the system (that is you and the other thing) is conserved.
The notion required here is the concept of system. A system is a set of parts that interact.
So, asking "If a force is applied on a body in an isolated system" is an ill-formed question. If the system is isolated, an external force cannot be applied to one of its parts. If an external force is applied to the system, the system is not isolated.
As you would understand, applying an external force to a (non-isolated) system changes its energy. Following the law of energy conservation, the energy that the system absorbs is the same as the one spread by the external component.
On the other hand, inside a(n isolated) system, a classical problem is the one of potential energy being converted to kinetic energy. In an isolated system, the amount of kinetic energy consumed by a subsystem (a part of the system) is the one that the rest of the system loses.