What is the output voltage of this 555 timer high voltage circuit?
Two notes:


the impedance transformation is the square of its turns ratio, the voltage transformation is the turns ratio itself. Hence your 1k/8r transformer will have a voltage transformation of sqrt(125) = ~ 11. But ...
the voltage transformation calculated this way applies to a sine wave, not to the on-off switching done in this case. Theoretically there is no limit to the voltage you can generate with this method, even on the primary (8r) side. For that reason circuits like this often use a zener diode at the primary side, to prevent damage to the transistor.