How to calculate the resistor value of a xenon flash circuit to be a set frequency
Steps:
Determine the breakdown voltage of the neon tube
Calculate when that voltage will be reached at C1 using R1/C1 to calculate the time constant
While it looks like R2/R3 form a divider that sets the time constant, before NE1 fires, it is an open circuit making the current through that leg 0, so there is no voltage drop across either resistor until NE1 fires, and at that point the SCR is triggered and the flash fires.
That will give you the (approximate) time constant.  Change R1 to change the flash rate, but be careful about the power being dissipated by this resistor. This will be temperature dependent.
If you need exact timing, replace SCR1 with an SCR Optocoupler, eliminate NE1 and drive the led on the optocoupler with a 555 or a microcontroller generating a 10hz pulse.
A possible optocoupler is the TLP548J(TP1,F) or the IXYS PS2401.