I am a bit confused on your setup, i am guessing that you had trouble with water flow because some tubes are higher than others? I can think of some ways around that (depending on the details of your setup) without using more than one pump. But I take it that you have the water flowing to all tubes evenly now, and just wanting to know how fast the water needs to flow.

I don't know any rules on that, other than you want the water to move so it isn't stagnant, but not so fast that backs up because the overflow system cant keep up (or damages the roots). But I would suggest a fast flow rate, because flowing and dropping water will add to the dissolved oxygen level in the water naturally.

HomeHydro,
all of the tubes are the same length, diameter and hieght. The problem I think is that the pump cannot produce enough pressure to pump all 7 adequately. When I made them two zones (4 pipes on one, 3 on the other), I was able to get decent flow.
I may opt to get a bigger pump (900gph maybe), and put it on the zone with 4 pipes and put the 650gph on the zone with 3 pipes. If the flow is too high, I can slow it down with the ball valves since each pipe has its own ball valve and union fitting so that it can be removed easily.

to get even flow rates, you need to make sure all the inlet valves recieve water from below. Otherwise you have issues water speed carrying water across "T"'s that makes it complicated.
I noticed the issue myself using a 650 on 3 lines. Never could get it entirely worked out. They all got enough moisture, just some got a lot more than others.
As for the flow rate, I wouldn't worry too much on it. a 1" out pipe should be plenty. Also, with the longer lengths you're using (mine are 5 footers), a faster flow will leave more oxygen in the water for the plants farther down the run.

You have made a parallel flow system which will take a lot of time and care to balance. The fluid mechanics of parallel systems are quite complex and the solutions are very math intensive.

yeah I racked my brain for ages trying to figure out why my second last tube wasn't getting any water and when I turn off the last tube the 3rd last tube became a trickle, still haven't figured out what is going on but a bigger pump sort of fixed it.

The way I look at it, it's all about even water pressure. And depending on the setup, I can see many different ways to balance it out. Of coarse the larger the setup the bigger the pump you may need. But as long as the water pressure from the water distribution tube is even. Weather it's a trickle or a flood, the flow in the first NFT channel and last would be flowing evenly.

Now of coarse, if you flood a tube from on end, and have drain holes along that same (level) tube. The water pressure where the water is pumped in, and the pressure at the other end wont be the same. Simply because the water is draining out before it can reach the other end, dropping the pressure along the way. But that can easily be reminded (depending on size and setup design) by simply splitting the feed line into more than one line. That way the water distribution tube fills from both ends and/or multiple locations from evenly spaced "T" connectors along the length of the tube.

Another way is (as long as the water distribution tube is level). By using a "T" connector placed in a upward position for each (NFT) channel, with a short tube straight up from the "T" connector a couple of inches. With a elbow connector at the top, and another straight tube. Then lastly another elbow connector to create a downspout into the NFT channel. This way even with only one water inlet into the water distribution tube the water pressurizes equally, and will overflow out the top evenly from one end to the other (as long as the water distribution tube is level). It's kind of hard to explain without using pictures, but I hope you get the idea.

To simplify things for large setups, I can think of even more ways to even the water pressure. Even including using inline "ball cock valves" to adjust water pressure from the pump where needed. Vertical setups aren't very difficult either especially when you consider that water always flows down hill. As for the water flow out of the NFT channel, that wont always be even because the roots of the plants can obstruct the flow.

Just as an update, I opted to just go with the one zone of 4 tubes. After 2 weeks of operations, I figured the flow rate is fine. I did opt to add two air stones being ran by one air pump (for an 80 gallon aquarium) for higher oxygenation.
My biggest issue to date is getting enough sunlight (out door greenhouse). Since I build the green house to be moveable, I moved it to the other side of the yard. This will allow the plants to get approximately 8-10 hours of sunlight, as opposed to 4-5 it was getting before.
I did my first solution change and increased the nutrients (using the Flora Series by general hydro).

Still working out the kinks as its all still new, but I think with the increase in nutrient concentration and 2X the sunlight, I should start to see better growth in the next couple of weeks.

Thanks for the help guys!