could i connect a flyback transformer directly to an ac power supply instead of a 555?
Uh. That's a really bad idea. What's your goal? If you are trying to make a tesla coil or something similar, you'll need to install secondary windings and use a dc power supply. Whatever you're trying to accomplish, you should be able to find some plans or schematics to guide you along. Edit- I once made a tesla coil that would light a flourescent lite bulb, create an arc that would solder metal and cause every tv set in a 100 yard radius to scramble. Caused a pretty good shock too. I used a flyback transformer and was able to generate an estimated 50,000 volts (it depends on what size tv you strip). You WILL need to add a secondary set of windings to the xformer and you will need about a 24 volt dc power supply rated at around 3 to 5 amps (and a few other components). You should be able to find the plans for a tesla coil on the net or at the library.
If you mean a line frequency supply, then no. Flyback transformers require high frequency to work properly, and they'll pass massive amounts of current if fed 50/60hz.
A flyback transformer is designed to work about 15 KHz with a lower primary voltage. If you connect it directly to the AC line, it will either burn up or pop a circuit breaker. Let us hope for the latter.
You can but you'll just blow up. That is if your not planning to kill yourself. What sort of a project is this. You must state specifically what is your main aim is here.
The frequency of an ac power supply is only 60 hz. That's way too low for a flyback. The resistance of a transformer depends on the frequency. At 60Hz a flyback transformer acts like a short circuit. It would draw a lot of power, might damage the power supply and nearly nothing would come out the other side of the transformer.