Put the car into drive and it will screech and then clunk and then move. Doesn't do it all the time (maybe only 1 out of 10 times) and only when shifting from park into drive. My first thought was a brake shoe hanging up but had the brakes inspected and adjusted. Happened to the mechanic when he was test driving it after working on the brakes and said it WAS NOT the brakes and maybe the torque tube or transmission. 

Putting it in this section per what he suggested where the problem may be. Idea what the problem is?

The clunk could be low trans fluid or a sticking valve in the transmission. But more likely it's the rubber support on the end of the trans crossmember. If you get under the car you will see a short metal piece sticking toward the inside at each end of the trans crossmember. It sticks in from the "frame" rail (the sill). The crossmember end should be about 3/4" ABOVE that piece, not sitting ON it. That piece is actually a channel that keeps the crossmember form going up or down too far should the rubber mount fail. After more than 50 years it probably has. Galvin's has replacements. When it fails the end of the crossmember moves up and down when going from park to drive and the end of the crossmember clunks.

The screech could be something hitting when the motor and trans moves, or just an old fan belt. Belts get hard with age and don't grip in the V groove so good. If they are old just replace them, even if they look ok.

I don't think so, it is more of a "cat's howl" instead of a belt squeal. When I put it in gear, it will screech, with the pitch increasing with me pressing on the gas, then "clunk" everything is fine. This only happens only the first 5 feet or so, if even that. That is what made me think the brake shoes were hanging up.

farna- seen your post after I posted mine. Will check out the mount and see the condition of that.

Well, it could be something internal in the transmission hanging up. Or the torque converter. Check everything else first. You might need to pull the torque tube so you can check that CV joint. It could be "flopped" to the side and slinging back in place, though I doubt it... never had one act like that before. One check for that is to jack and support the rear end then put it in gear. Does it still screech? Then the issue is in the drivetrain. If it doesn't, it's in something that rolls, like the brakes or something rubbing a tire or wheel. The tie rods are very close to the wheels on some of these, so it could be a wheel weight or wheel edge scraping a tie rod, and when the tie rod rotates a bit from the scraping it stops. THAT I've had happen -- a thin 1/8" spacer may be all it takes to fix it. Also, could it be the starter hanging up? If the Bendix drive doesn't disengage it can make noise. It would do that whether the car was moving or not though.

If you suspect the transmission it could be expensive. CHECK THOSE RUBBER MOUNTS ON THE CROSSMEMBER FIRST!! If one or both have collapsed that could be the whole cause of your issue. You can try cutting a couple wood blocks as spacer and put one on top, jack up the crossmember, and wedge one in the bottom (between the channel and CM on top and bottom) so it won't move. The driver's side is usually the one that causes the most problem. I'd wedge that one and see if it doesn't reduce or eliminate the problem.

If that doesn't work, you can drop the trans pan and pull the valve body, take it apart, and thoroughly clean it and the pressure regulator. Don't do this without a TSM!! You can also adjust the bands while in there. If that doesn't do it, the trans will need to be rebuilt and the torque converter checked. Bearings going bad in the converter can do what you describe. I'd suspect that before the pump. If this doesn't do the trick it's time to rebuild the trans and/or converter. Pull both and have converter checked first. When you drop the pan you may have a clue -- lots of metallic shavings in the pan/oil indicates something has been grinding itself apart... Have the converter checked before rebuilding, you might be lucky. At that point I'd really consider having the trans rebuilt anyway, but budget might not allow...

It's remotely possible that a converter or flexplate bolt has come loose.

and AMX007 with low fluid.

Another thing I have noticed is the car will shift "hard" into gear. Put it in drive or reverse and the car will "jump". Seems to shift smoothly once in drive.

65-66 V-8s used a cable, all others a vacuum modulator.

It's starting to sound like a hard failure of something inside, maybe the sprag clutch (a one-way clutch). If everything is intact underneath I'd proceed with dropping the pan and a thorough cleaning of the valve body and pressure regulator assembly. If that doesn't do it, it's rebuild time.

I will take a closer look at that. 

No problems before this spring so didn't want to start adjusting something that didn't need to be adjusted and really mess things up. 

Just wondering why it would be a very intermittent problem as if something wasn't adjusted right I would think it would be most of the time. 

Looks like I will be contacting the transmission shop and see if they have even heard of a BW Flash-O-Matic.

Or the Ford FMX. The FMX (and earlier Ford autos) are license built Borg-Warners. There are some internal differences, but many parts interchange, and if they have experience with those they will be able to handle any BW model. Volvo used  Borg-Warners through the 80s, a variant of the M-35 up through around 76 or 77. The later model BWs (50 and 60 series) are a totally different design, more akin to the AW4.

I'd get a TSM if you don't have one, and send it to the shop with the trans even if you pull it yourself and they don't think they need it. I did that once, and the shop thanked me when I picked the car up. Said there were a couple things that wasn't covered well in their trade manuals and the TSM came in handy.