Would the FCA47N60F work for a ZVS flyback driver?
You haven't provided any measurements taken on the circuit with the original parts, so it's pure speculation why the old ones failed. Excessive power? Bad gate drive? Avalanche? Excessive dv/dt? If we knew what killed the old FETs, it makes choosing a replacement much less based on guesswork.

On paper, The Fairchild parts are "better" in several key areas: \$V_{DS}\$, \$R_{DS(on)}\$ and avalanche capability. However, the total gate charge is higher, meaning the device will switch slower than the original part.

In my experience, it's very difficult to judge solely based on paper. I've seen MOSFETs which "look" better in all areas end up burning more way power than the originals, or fail catastrophically. Since several parameters appear better, try the substitution and see if your reliability improves.