If the specific transformer mentioned in the schematic is not available to you, any transformer with the specifications primary 117VAC, secondary 6.3VAC CT (center-tapped) should work.
In this case you might have to choose a different drive frequency in order to operate at the sweet spot of the transformer: "[...] I found in driving a transformer as is done in this project that the overall performance varied significantly as I varied the drive frequency. In a series of experiments I loaded the transformer directly with a variable resistor (no rectifier used), measured the AC voltage across this resistor, measured the DC current into the transformer, and varied the drive frequency. I looked for a frequency where the output voltage was highest and the input current was lowest. [...] 'ripple' is roughly +/-25V for output voltage >200V. This ripple isn't sinusoidal at all. It is basically a spike then monotonically decays until the next spike."