Its been a long time since I did any fluids, and even then, it was not much. But I'll take a shot just from simple logic.
Suppose we have a single fan at the front end of the duct. It is rated for 650 CFM, and without any duct there, you will get essentially that. But suppose you put this fan in a duct. Moving air will see friction against the walls of the duct, slowing down the air flow. The back pressure reduces the flow, so you really don't get a full 650 CFM out the end of the duct. Of course, bends in the duct hurt even more, but you said it was a straight duct.
Now, suppose you add a second fan at the tail end of the duct. This is sucking air out at a nominal 650 CFM rate too. But in the end, all it does is give you something closer to the full 650 rating for the two fans. You don't get 1300 CFM, you get roughly 650 CFM.
With two fans in parallel, both feeding into the duck (or both pulling air out) if they are not limited by air flow through a duct that is big enough to handle one fan, then you might get more air through in theory. But the problem is, now you have higher velocity air. The link that gregmac provided tells us that pressure losses are proportional to the square of velocity. If you could double the velocity (and in order to double the air flow, you must double the velocity of the air as it moves through the duct) then you would quadruple those frictional losses.
It gets worse. As is pointed out in gregmac's link, with two fans right next to each other, the air flow into those fans will interfere with each other. So you really wont achieve the full rating for those fans if they are set side by side.
How about the 800 CFM fans? If they are too big for the size duct you have, then you again will be limited by the back pressure. You may end up with only a net of 650 CFM anyway.
It seems to make most sense to have a second duct. Run two ducts in parallel, both adequately sized for the fans they are fed by. Yes, I know this may not be an option.
Such a connection introduces more friction to the system, reducing the available flow. If the system is sized adequately to accommodate this, then yes, it is OK. If I understand you correctly, this large round duct you are connecting to the air handler is serving as an extended plenum. Partly depending on the relative size of the duct and air handler, this may be the one place where it would be worth constructing a proper transition fitting instead of a simple flat adapter.
In a way, the flat adapter is crippling the entire system before it even gets a chance to get going, just my opinion, based on my innate desire for efficiency. As stated earlier, if the system can accommodate an inefficient transition, then it is OK to use it. I just happen to not like it.
Best Answer
Fix
If the pipes have been deformed (by placing something heavy on them, for example) then you can try bending them back to a round shape. If they're deformed to the point they actually have folds or creases in them, I'd give up and throw them out.
New ducts
Round ducts are sold as sheets with a special fold along the two sides that interlock into each other to form the round shape. They're actually very easy to assemble, and not very expensive. Most big hardware stores will have a few sizes in stock, in addition to elbows, boots and other parts.
You mentioned you don't have enough now anyway, so if you buy a few new pieces, you might be able to use their round shape to fit your existing pieces into.
Re-crimp ends
You can also get a duct crimping tool to redo the crimps on the end, making them tighter so they fit into the next piece over.
Personally, I've done several modifications/changes to ducts like this as part of basement, garage, and laundry room renovations, and though I'm generally always happy to have a an excuse to buy a new tool, I've never bought a pair of these.
A handful of times I've had to make a crimp more tapered to fit pipes from different eras together, and a couple times I've had to completely make my own crimp, but I've just used a pair of long needle nose pliers -- grab on, twist 45 degrees clockwise, move the pliers over 1/2", repeat until you're back at the start. It doesn't look as nice but it's totally functional. Just be careful of having too much protrusion into the duct as it can disrupt airflow.
Ideally all your crimps are also facing the direction of the airflow, but this isn't always possible.
Connections
You can use 1/2" self-tapping screws to attach ductwork together, usually a couple is all it takes. For dryer vents, it's better to avoid screws as lint will catch on them and block the pipe.
Don't forget to tape the seams using aluminum foil tape (not regular duct tape, which is not for heating ducts!). If there's no chance of the ducts being mechanically disturbed (eg, they're in a joist bay, secured by hangers) I've often only used duct tape (no screws) to attach them, but I don't know if this is kosher.