Granted fly-back conditions would occur in a transformer setup would it really be producing any significant current at those power rating? I would not call it a fly-back setup, but only because any fly-back current is secondary to main transformer power transfer.
Where do I start?
The 4017 drives one MOSFET for 25% of the time, then turns off. During this time the output goes positive and then starts to go negative.
The amount of negativity will be discussed later.
The energy from the negative excursion comes from the collapsing magnetic flux.
We can call this "fly-back" or "controlled fly-back" or "collapsing magnetic field." At least it is energy being delivered to the output when the input is not being driven.
Now the other MOSFET is turned on the flux in the transformer, (that is already collapsing) will be driven in the same direction to produce a negative output. After another 25% of the cycle-time, this MOSFET will be turned off and the flux will collapse and when it is approximating zero output volts, the other MOSFET will be turned on to produce the positive portion of the waveform.
Your comment
would it really be producing any significant current
is yes, as the waveform at this portion of the cycle has an area under it that represents “power” or “energy.“
Now we come to the “turns-ratio” question.
Since we are putting 24v DC into the primary, we need to have a primary with the correct number of turns for a DC value.
If it is 6 turns per volt, we need 24 x 6 turns.
The secondary will produce one volt for each 6 turns and since you want to produce the same amount of energy a 110v AC supply will deliver, you will need 110 x 6 x 1.4 turns.