First, for 10A output current, flyback would be totally the wrong choice due to high losses on output windings and high flyback spikes to the primary. Two-switch flyback may be a good choice but still the output winding is the issue for 10A current. Go for either two-switch forward, half bridge or even LLC half bridge.
Designing a variable output SMPS is a challenging task:
The first problem comes from generating supply voltage for the controller block: The auxiliary winding concept in conventional isolated converters is totally useless for variable SMPS, because the output voltage of this winding will be load- or output voltage-dependent. So you'll need a separate supply. Actually, a self-oscillating (also known as "Ringing Choke") converter with, say, 15V/200mA output will do the job. But, as you might guess, cost and placement issues... Still it's the best solution.
The another problem is generating 0V. IIRC, some articles about this tells that a negative reference is needed. But I'm not sure. Anyway, if your minimum output voltage requirement was 2.5VDC then simple TL431 and divider network with a linear pot would simplify the design.
And the last problem is light load or even unloaded state. For forward and half-bridge, you need an output inductor. It's easy to get 10A output from a 33uH toroidal inductor with a switching frequency of 100kHz. But what if the output current goes down to 10mA (Suppose you want to test an LED with your supply, for example)? You'll need either an output inductor with high inductance (say, 1mH) or a heavy dummy load to waste some of output power for unloaded state which decreases efficiency. LLC half-bridge does not need an output inductor but even for this, you still need to waste at least %5 of max output power on a dummy load. Of course you can get the converter working with 12VDC/10mA output even with %1 dummy load, but if you decrease the output voltage then the converter will enter discontinuous mode and you'll see that the output voltage is fluctuating.
Rather than output voltage, you'll also need to regulate output current (for current limiting or output shorting). This will need an extra comparator which brings extra care for designing output and feedback blocks (feedback stabilization).