I'm aware of two different styles of flex plates used with the Fordomatic transmissions.
One was used with the air cooled units (look for a finned aluminum torque converter) and the other was used with the later trans that ran the cooling lines to the radiator. The later oil cooled Fordomatic transmissions (April '56 up, IF I remember right) have a smooth steel torque converter.
You may have more than one thing going on, too. A loose flex plate where it connects to the torque converter is a possibility... cracked or broken 'tabs where the flex plate connects to the torque converter are a possibility if things were loose and have been 'working'. You also may be having trouble with the Bendix on the starter... and if that's been acting up the ring gear on the torque converter may have gotten chewed up.
Now that I've come-up with some awful things that can happen, you need to remove the inspection cover from the bellhousing and see what you can see.
Hope this is of some help.
NoShortcuts
a.k.a. Charlie Brown
near Syracuse, New York