Misunderstanding about flyback transformer and turn ratio
The first error is in assuming the 24 volts is produced by all 16 secondary turns - look at the first tap point at the top of the 6 turn winding - this is the ground reference for those voltages. In other words the 24 volts is produced from 10 turns and not 16: -



I would say that the next error is in assuming that the minimum supply for the primary is 290 volts. This may not be your error but someone else's. Given the turns ratio of 52:10 to make the 24 volt output, I would say that the minimum DC supply on the primary is more likely to be 125 volts DC or around 87 V RMS after accounting for the bridge rectifier. It's likely that the minimum supply is 87 volts AC because that just about makes the transformer suitable for 85 to 264 volts AC i.e. the universal supply range of 85 - 264 V RMS.