To expand slightly on the answers by @The Photon and @Dheeraj Gujrathi, the dominant contribution to the kinetic energy of the electrons in the circuit is the thermal motion of the electrons. That energy typically increases in resistances in the circuit (resistors, long wires, etc.) and we track it as thermal energy, not as kinetic energy.
The additional motion of the electrons due to what is happening in the battery is what we call the "drift velocity" of the electrons. In any typical circuit (copper wires, resistances of a few Ohms or more) the drift speeds are tiny. Values of mm/s or even $\mu$m/s are pretty typical. As a result, the additional kinetic energy in the circuit due to the drift motion of the electrons is negligible. So, it is rare to even talk about any increase of kinetic energy in a circuit. We talk about chemical energy in a battery being converted to thermal energy in resistances, and being stored as electric potential energy in capacitors (and magnetic potential energy in inductors). The only time we would have a circuit with non-negligible kinetic energy would be if some circuit element is basically a particle accelerator, such as a cathode ray tube (old-style TV screen), a fluorescent light, an X-ray emitter, or something like that.
You replied below with
suppose a capacitor is being charged with a resistor between the +ve terminal of battery and one of the capacitor plates, as some charge flows through the resistor, heat is produced, some of it is lost to the surroundings, while some of it increases the kinetic energy of the electrons(vibrational energy), so as these electrons then go and stop at the capacitor plates, where does there thermal energy go? Do the electrons still retain their vibrational(thermal) energy at the capacitor plates?
I tried to reply with an additional comment but found that I couldn't make the comment short enough to fit. So here's my answer to your comment below.
That increase in the kinetic energy of the electrons which you are calling "vibrational energy" is thermal energy. It didn't go anywhere, other than perhaps into the environment as the wires and resistor equilibrate to the temperature of the air around them. Typically once energy has been converted to thermal energy it is difficult to convert it to any other form. Difficult, but not impossible. That's what a lot of a thermodynamics course deals with. But in this situation all the energy that becomes thermal energy will remain as thermal energy.
So, let's track (simplified...) the energy conversions which occur in the circuit.
In the battery chemical energy is being converted to electric potential energy.
As the electrons move from one plate of the capacitor to the other they pass through the resistor. Some of the electric potential energy they have gained will be converted to thermal energy in the resistor. Once it is thermal energy it stays as thermal energy. It will now be transferred gradually to the surroundings, but it won't convert to any other form of energy.
Some of the electric potential energy that the battery produced will be stored "in" the capacitor. It is probably more correct to think of it as being stored "in" the electric field between the capacitor plates. Alternatively, you could think of it as being stored "in" the position of the electrons in the same sense that a mass raised to a larger height has more gravitational potential energy due to its position.
That's it. That's all of the energy transformations going on here.
However, all of the picture I've painted above is, in some sense, "lies told to children". The picture of the energy being "carried" from the battery to the resistor and the capacitor by the electrons has some major flaws. A much more correct picture is that electric and magnetic fields are produced in the vicinity of the circuit, and the energy transfers from the battery to the resistor and the capacitor via these fields. This does result in small motions of the electrons which collide with atoms in the resistor causing the conversion to thermal energy there, and small rearrangements of the electrons which produce the E-field in the capacitor, resulting in storage of electric potential energy there. To get a nicer idea of this more correct picture, have a look at the YouTube video that Veritasium did a while back. That video is a bit controversial, but I would say not controversial among people who really understand electrodynamics.
