C8 charges when Q2 turns on, which will probably defeat the peak current mode operation of the controller.
They also don't document it very well, but TPS40210 goes into hiccup mode (/SS pulls low, stays off until crosses rising threshold) rather than current limiting. It's rather dumb.
The combination will probably frustrate operation of this circuit enough that it never starts up, or doesn't maintain the full output you were expecting, or isn't able to recover from a momentary overload condition.
You can use multiple secondaries as their own flyback outputs, and connect the DC outputs in series. Then you don't need C8 charging on the "down stroke", energy gets delivered to the output only in the flyback period (Q2 off). Probably use N = 2-3 of say MSS12xx dual-winding inductors, with the primaries in parallel, and the secondaries wired accordingly. (Choose inductance to be N times higher per inductor, because for uncoupled inductors, the value reduces in parallel.)
Tim