Transistor Driving Flyback Failing Below Ratings
Unfortunately, a flyback requires ratings for a transistor waaaaay above what you would niavely expect.

The venerable old 2N3055 is specified to only 60v on the collector. The TIP35C mentioned in the video is 100V rating, but even that is rather low for the suggested configuration.

When you operate a flyback, the rise in collector voltage is determined by the energy stored in the primary inductance, and the capacitive load connected to it. It's not uncommon for TV flybacks, and auto ignition coils, to develop 300v on the primary, and therefore the collector of the driving transistor, when driven from a 12v supply.

It helps to measure the collector voltage with an oscilloscope, as the power supply voltage is raised.

There are several things you can do to avoid failure due to high collector voltage ...

a) Use a transistor with a higher voltage rating
b) Increase the load capacitance, to absorb the inductive energy at a lower voltage
c) Use an overvoltage clamp diode collector to emitter (inefficient)  

... but it's all a bit hit and miss without an oscilloscope, so you can actually see what's happening.

You may get shown videos of 2n3055sTIP35Cs working in this configuration, but if their transformer is a bit soggier, or their transistor is a bit more robust, theirs could work OK, and yours fail.