The auxiliary winding never has much current in it. It is the voltage that is important.
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I'll explain the circuit as I understand it. I'll have to guess some voltages because they depend on the turns ratio of the transformer.
When the circuit is energised, all the capacitors will be discharged. The voltage at 1 will be the same as V+, and all other voltages will be 0. Current will flow from V+ to 2 through the 1M resistor. That current will flow through C2, charging it up, and though the 220 Ohm resistor and the auxiliary winding. Neither the resistor nor the winding will have any significant voltage drop across them, so 3 and 4 will stay at 0 V.
When 2 gets to about 0.7 V, the transistor starts to turn on, so the voltage at 1 falls. As it does, the voltage at 4 and at 3 rise. C2 is still charged with 2 being about 0.7 V higher than 3, so this makes the transistor turn on more, so very soon, much less than a microsecond after the transistor started to turn on, the transistor is on fully.
Now 1 is at 0 V. I'll guess that 4 is at +10 V. 2 is still at about 0.7 V and 3 is still at about 0V, so there is 10 V across the 220 Ohm resistor and so around 40 mA flows, starting to charge C2 the other way, and keeping the transistor turned on.
With 40 mA flowing through C2, the voltage across it will be changing at about 10 V/us, so in about 1 us it will be charged to 10 V and there will be no current to keep the transistor turned on. If there is a lot of current in the primary winding, that current will be flowing through the 47 Ohm resistor, increasing the emitter voltage on the transistor, so 2 will have to be at a high voltage for the transistor to say turned on, so it will turn off sooner. Also the transformer may start to saturate, which will cause the current to increase faster, and the voltage on the auxiliary winding at 4 will reduce.
Anyhow, there is now a significant current flowing in the transformer primary winding, so there is significant magnetic energy in the core of the transformer, and the transistor is just starting to turn off. Because the voltage across the primary winding is reduced by the transistor turning off, the voltage at 4, which is produced by the auxiliary winding, is also reduced. Because C2 is now charged to about 10 V with 3 higher than 2, as soon as the voltage at 4 reduces, so does the voltage at 2, turning the transistor off very quickly.
Once the transistor is off, the voltage across the windings reverses, so 1 goes higher than V+, and 4 goes negative. The voltage at 6 will go positive, and current will flow through the IN5402 and start to charge the output capacitor. The output of the auxiliary winding also goes negative, so 2 goes negative, limited by the 1N4148, and C2 is charged the other way, so that 2 is at a more positive voltage than 3.
When the energy from the core of the transformer has all gone, the process starts again. Because 2 starts at a more positive voltage than 3, once the process has been run once, the current through the 1 M resistor isn't needed.
There are a couple of other points about this circuit. The auxiliary winding seems to have the same number of turns as the output, as they are labelled as having the same inductance. When the voltage at 6 is +ve, the voltage at 4 will be -ve, but the same magnitude. As the capacitor on the output is charged, the capacitor at 5 will be charged to the same voltage, but negative. (The capacitor is shown the wrong way round). When that gets to about -5 V, the zener diode will turn on and take current from the base of the transistor, preventing the transistor from turning on. That means that the output can't exceed +5 V, so the output is regulated. It may not be very good regulation.
The idea of the 1N4007 and the 10 nF, 1kV capacitor (labelled 103 1kV) is to absorb the switching spikes from the transformer. When the current in the transformer is stopped quickly, imperfections in the transformer, called "leakage inductance", means that some of the transformer's energy has to be absorbed from the primary. Most will be absorbed in the output capacitor, but some is on the primary. The capacitor absorbs that energy. The circuit is missing a resistor to discharge that capacitor. It will need maybe 100 kOhm in parallel, or it will get charged to a larger voltage each time the transistor switches off, so that would end up not absorbing the spikes and that transistor would be damaged.
I hope this helps.