I have a 1966 Fury 3 that cranks and gets spark but will not fire for some reason! I've checked the coil and points all appear in working order. I'm stumped!

 

The big 3. Compression, ignition and fuel.
You said you have ignition.
If it's not flooded, Check to see if the choke is closing. If that's ok give a spray of fuel down the carburetor and see if you get a start from that.
If it ran ok prior to shut down the timing chain could have jumped a few teeth, that's when they skip a beat on shut down.

 

Make sure you don't have the distributor in backwards (180 deg).