"Flyback" transformers,(more correctly called Horizontal output transformers),in TVs & Picture Monitors normally operate at around 15kHz with specifically shaped waveforms.
These transformers do several things beside the generation of EHT,such as to drive the Horizontal Deflection coils & also provide "boost HT" of around 150v which is ,in turn,used as the supply for the horizontal & vertical output stages.
We aren't "getting something for nothing",as the power to do this all comes from the lower voltage fixed supply.
In your circuit,you don't have the advantage of "boost HT"& have to live with your +24v.
From my calculation,the 555 produces a rectangular wave at a frequency of.20.57 kHz.
Horizontal Output transformers are quite "fussy" about what frequency & wave shape they are driven with,& efficiency will be poor.
I suppose you could shift the frequency to 15kHz,but that is perilously close to the Audio range,& you will have problems with intermodulation.
Even 20.57KHz is a bit marginal.