I've made the Tesla coil but in the back of my mind I knew something is wrong. The flame produced by mine Tesla coil was less powerful than that I bought or saw on Youtube. That lead me to a conclusion that is not the end of the project. 

So, I decided to start from the beginning. In the simple form, we start with one coil and MOSFET. Let's put a short pulse on MOSFET's gate. 

What happens? (Blue is gate driver output, pink is coil output)

Oscilation!? Why? The MOSFET'S gate is at 0v, source and drain are cut off. Why something should happen? Well, there are a depletion in the transitor as there is voltage over it. So the coil with transistor makes LC circuit. (Since the depletion layer depends on voltage applied, LC oscilation frequency changes as power supply voltage changes)

Now it's clear why there are some frequencies for the main LC  that works and other don't. 

If the input coil (and MOSFET) frequency and main frequency are multiple of each other then main LC can build up high voltage, otherwise it doesn't and all the circuit is not working or low efficiency. 

Actually, once main LC is connected to the input coil, input coil frequency is charging but at least now we know the range.

So, in my case I've used main coil of 2.4uH and 100pF multi mini capacitor. This LC gives frequency of 10.4MHz. 

Main coil dimensions are diameter of coil 32mm, wire diameter 1.3mm number of turns is 9. 

RFC coil dimensions are: coil diameter 60mm wire diameter 1mm number of turns is 9, which gives 6uH. Since irfc output capacity is 600pF (plus equivalent capacitance of main circuit is 700uF) and and RFC coil is 6uF the frequency is 2.45MHz, which is 1/4 of main frequency of 10Mhz. 1/3 of main frequency gives the same result of 2Kvolt on main LC circuit. Some manual fine tunning can increase voltage to 2.5Kvolt.