Look at the data sheet for the 2N3055 and note that the maximum power dissipation is ~115 W with an excellent heat sink, and that the maximum current rating is 15 A. 12 VDC at 15 A could theoretically produce 180 W out, but that would be for a "perfect" switching device with no dissipation. This circuit does not use the most efficient switching mode, so considerable power is wasted in heating the transistor.
That said, the circuit you show, apparently from Instructables, should work, actually producing a few thousand volts at a milliamp or two... far less than your suggested 600 W. This is a good thing, as one could get serious RF burns from a 600 W RF supply.
To get higher voltage, bypass the resistors with capacitors, as shown at PocketMagic. To get yet more voltage, the primary of the flyback transformer should resonate with the secondary, using an experimentally-determined capacitor.
If you make it, use a larger heat sink than that shown -- perhaps a heavy aluminum fry pan, with bottom filed flat. Use thermal compound, as well. In any case, don't expect the transistors to last very long, particularly if you use more than 12 VDC. If they don't fry from overheating, high-voltage transients on the primary will likely destroy them.