After new points and condenser, static timing, and a switch to control the starting carb function, I am still having a back firing through the exhaust at idle. The car starts well cold and has the hissing from the starting carb when cold. After 10 minutes or so I'll shut the starting carb off and the engine slows down and then starts to back fire through the exhaust. It also won't stay running unless I keep my foot on the gas pedal. I have not checked my plug wires but I don't seem to have a misfire. My dist cap looks new. Any thoughts?

 

I will start off with the obvious.
Although you say you have statically timed the engine it could be that the timing is out and one cylinder is firing when the exhaust valve is open. Get a timing light and do the timing accurately.
Have you double checked your firing order. The six-cylinder Jaguar uses a unique 1-5-3-6-2-4 firing order with the No. 1 cylinder located closest to the bulkhead. Two HT leads crossed will give you firing in the cylinder at the wrong time. Sometimes hard to follow the HT leads because of where the Dizzy sits so disconnect them all and start again. Put a piece of white electrical tape on each end of the HT leads and number them so each lead is numbered top and bottom. This way you know the lead numbered one on the dizzy is going to cylinder one at the back of the engine and so on.
Too rich mixture which could result in excess fuel being pushed into the exhaust port and then igniting causing the back fire. Could account for the poor idle. This would be easy to sort out by tuning the carbs with a color tune kit.

Going deeper into the engine it could be a bent or miss seated valve on the exhaust side so when the cylinder fires it is firing through the exhaust. Have you done a compression test on the cylinders as it could eliminate this as a fault.

 

if an engine is running well when choked and rough when the choke is removed after 10 minutes, i would assume the carburetors are set too lean.

 

Agreed but let the OP sort out all the basics Cass recommends first.
Also see related thread below. Same car, same subject. Some other basics below. Riveted rotors have been an endless cause of trouble as have failed capacitors/condensers etc.

http://www.distributordoctor.com/rotor_arms.html

 

It's a fuel problem.
The engine runs OK on the starting carby.
After shutting off the starting (thermo) Carby it then starts to run rough and needs to have accelerator applied to stay running.
The starting carby system distributes an air/fuel mixture equally across the whole intake manifold via pipes under the intake manifold
When the starting carby is shut down it sounds like one carby is not feeding and the engine is trying to run on 3 cylinders, hence the need to apply accelerator to keep it running
The back firing in the exhaust is also a sign of an over lean mixture. Detonation occurs when the air/fuel ratio is too lean
Most likely a stuck Carby float needle not feeding a float bowl or a blocked jet.
I would check the rear Carby's float (the front Carby float is feeding the thermo Carby) and if that is OK then check the jets on the carbys for blockage

 

I Think you have hit the nail on the head Bill. Makes total sense if you have spark at each plug which you obviously do enriched by the cold starter carb (AED).