this might not be the best job for flyback - look at all combinations of vin/vout, you will need weird transformers to put it all on one block - many of national's products are built for one customer, not so good for general use.. (they have nice tutorials though!)
i would reccommend boost, boost, charge pump, buck in your order.. this takes more components but efficiency is high and these components are easy to find, compared to the weird multi-coil transformer that a flyback will require..
Have you built many DC-DC? You are familiar with each topology? In buck topology (Vout lower than Vin), you put a switcher between Vin and your inductor. Switcher allows little packets of power into inductor and output - if you need 2A!! on your 5v rail you MUST separate this system from your other supply, else they will ripple a lot due to how hard 5v rail is working.
In boost topology, the switcher comes after the inductor.. Switcher pulls inductor to 0v for a little while, then lets it spring up to high voltage - a diode makes sure the higher voltage is directed to the output. Both boost and buck are easy to work with and very high efficiency (>90%). They can also provide LOTS of power - good workhorses.
If you only need 300mA on -15v rail, I say build a 600mA +15v boost, then take half of that power and invert to -15v with a charge pump. A charge pump charges a capacitor to +15v, then flips it over to instantly give -15v. Also high efficiency, but only 80-90%.
A flyback will put all of these together into one transformer. You switch one side with 7.2v, and many other secondary coils will provide your other voltages. But they all need to be perfectly synchronized - hard to do if you need to make your own transformer.. Say 5v lead is a little too high - then flyback switcher will go a little lighter than it should and all other voltages will droop. With multiple regulators they are all independant! You can buy 3 of the same regulator chip, and adjust them all to different voltages with only resistor divider.
Let me know if you get this, I can refer you to some data sheets.