Heat energy flows from one particle to another because heat is really just the accelerated movement of subatomic particles that bump against neighboring particles and cause them to move faster in a process known as conduction. Heat energy is really just kinetic energy in very small particles. However, heat can also be said to flow with fluids during convection or transfer by electromagnetic rays via radiation.
Heat energy flows as heat energy only through conduction. Convection and radiation also move heat, but do not themselves exchange heat energy between one particle and another. Convection is the movement of a fluid containing heat energy. This fluid carries heat energy with it and either releases it as electromagnetic radiation or conducts heat into a cooler object.
Radiation is a direct movement of energy, but the energy is electromagnetic energy, moving via photons like light, not kinetic heat energy. Hot particles convert some of the kinetic heat energy into electromagnetic energy that radiates out. When the radiation strikes another object, some of the electromagnetic energy is absorbed and converted back into heat energy. Thus, heat can only flow between two particles in contact with one another or after being converted into another form of energy that travels between objects.