Can flyback transformer used for push pull converter?
If you use a flyback transformer in forward converter mode, you'll be faced with an unusually high magnetising current, due to the transformer's low primary inductance. This is not necessarily a job-stopper, it just means that the primary drive devices will dissipate more than you would expect. With a big enough low ESR input capacitor, and low enough RDSon devices, there's no reason why you couldn't make an adequate design. 

An alternative would be to resonate the primary with a capacitor, which then sources the magnetising current, and drive the primary at resonance.

The leakage inductance also tends to be higher, at least as a ratio to the other inductance.

You'll already have discovered from your research into flyback transformers that they tend not to have a centre tap, which is needed for the simplest two-device push-pull drive. A single winding will need to be driven with an H-bridge.

It would be best to source a proper forward transformer. Ungapped cores are easy enough to buy, and with few turns needed at high frequency, they much more practical to make than mains frequency ones. Design considerations are different to mains frequency ones though, so be careful where you get your equations from. Peak flux tends to be determined by heating at operating frequency, before getting limited by saturation.