So trouble shooting 101 - you say the engine ran "outside" the car? Did it run well? If yes, then what did you change when it was then installed in the car? These are really pretty simple devices. Make sure everything is connected, all vacuum ports either plugged or connected and put the old carb that it ran with (assuming it ran well) back on and start it. You do not need an accelerator cable - screw all of that. Just hand prime and try to start it. If you have changed a bunch of stuff since the time the motor was last run, then you have to go backward to see what may have affected this. OBTW, the picture at the top of this tread certainly is not a new cab with all the black carbon buildup on it. A base properly tuned 351C at idle should pull approximately 17.00 inches of mercury (vacuum). The vacuum gauge needle should be rock solid - no fluctuations. Depending upon what you read (once you get the thing even running) will tell you much more as to what else might not be right (timing, vacuum leaks, plugs, etc.). A motor that is backfiring that much and flames out the exhaust sounds like either a massive fuel leak from the top end or a stuck value that is causing major running issues.
Perhaps you can walk us through the progression of the motor and how it ran outside the car and then the installation and what changed.
Here to help if we can.