TI's datasheet does a good job of explaining the controller architecture so I won't cover that. Additional guidance can be found in application notes AN-1481 & AN-2292. Instead I'll focus on those aspects specific to this implementation.

Main inductor. I wound my own inductor on a Magnetics MPP core because I couldn't find anything off the shelf meeting my spec; if at all possible use a commercially built one (unless you are really good). The secondary winding is not regulated which makes it very sensitive to leakage inductance. In other words, output voltage regulation is dependent on this. This is the reason for the 11% V2 regulation spec. I only got this after three different cores and six winding configurations.

If you do build your own inductor try to keep the turns ratio and overall # turns low. This spec uses a 2.6:1 ratio for the secondary which is a likely limit. A high number of turns / ratio increases leakage inductance. The winding build itself (layers, wire, etc.) also has a huge influence and this is discussed more in the <build> log.

V2 snubber (C18, R8). These were added during evaluation to reduce the leakage inductance ring. This trace shows the unclamped ring.

Although it did not appear to materially increase D2's dissipation I elected to add it for reduced EMI. Trace below is with snubber installed.

At higher input voltages R8 will dissipate ~ 250mW.

LC filters. The input and both outputs include LC filters to reduce ripple and switching spikes. The values for these were obtained empirically by observing the frequency spectrum in the outputs without filters and then calculating the minimum required inductance. A larger value was then selected based on size & saturation margin. Resulting worst-case AC ripple (CH1=V1, CH2=V2):

Input capacitance is sized to minimize input current ripple and for convenience I used the same inductor to filter switching spikes.