I have a lashup high voltage supply assembled using a Tv lopty, the primary is wound around the core using just a few turns, a lot of them allow you to do this.
However the circuit is a bit more complex, it uses a smps Ic, however the o/p is regulated, not sure what the max o/p is, I set it to the most the resistor divider would take sensing the o/p voltage.
You could however do something simpler.
If I got it right the system chem was talking about uses the trigger trans in a flash circuit, the circuit charges a cap up to about 300v, then a thyristor dumps this into a trigger trans primary, causing 4 - 6kv on the trigger trans sec.
Only a few milliwatts at most will be produced, but if your using this for thermionics or something that might be enough.