This is probably the most well known flyback transformer driver circuit. It uses two 2N3055 power transistors in a push-pull oscillator configuration. The value of the resistors is not that critical. In fact you can even use a 1/2W for the 27 ohm resistor, but it may burn out if it is left to run for a long time. This circuit will accept voltages up to about 24V, but I would not go any above this as you risk destroying the flyback transformer. Link