How to choose mosfet for DC AC flyback
You select your mosfet based on on the max voltage, current, rdson and timing requirements to name a few. Find the max voltage at that node and the max current that will flow through the part. Then go on a distributor site and find a mosfet that will work. 

As far as your circuit goes, a mosfet will not work to switch the input transformer because it can't handle the negative current (usually mosfets come with reverse protection diodes) when the voltage goes into the low part of the cycle. You need a triac, or relay or something that can handle the reverse votlage.