Flashing check engine light

From the description I would think one of two things. The first is that the misfires loaded the exhaust with raw fuel. That could cause the rough running as it's trying to burn that off and causing the fuel mix to go crazy as it tries. Second would be if the raw fuel overheated the catalytic converter enough that it fused the substrate and it's blocking the exhaust flow, that would cause rough running and the smell.
As a test I would remove the front O2 sensors and start it, if it runs better then you will need to check the exhaust system for blockage.

This shows a few tests that could help:

https://www.2carpros.com/articles/how-to-test-a-catalytic-converter

Does it also have white smoke out of the tailpipe? Or if you hold your hand over the exhaust is any coming out?

The sensors can be different on that truck depending on which emissions system it has. The federal version has 2 sensors while the California version has 4, the ones to remove will be the first ones in the pipes coming from the exhaust manifolds. Those are also the ones you test in.

The muffler and back tailpipe came apart, right where the hanger is. Also I hear like a whining noise under the hood. Husband doesn't here it. We had a small oil leak, it now seems a little worse. Also when he took the plugs out, there were a few that looked white, if that makes any sense.

White on the plugs sounds like fuel washing them clean. It could also be coolant but we need to start the testing process from what symptoms it has.

There was a coolant leak, fixed it, new water pump, alternator, radiator hoses, serpentine belt. What is the testing process? Husband is ready to just buy another Jeep. I don't want to, in the last few months we almost $3,000.00 into it.

Doing the exhaust pressure test and seeing what the engine does with the sensors out. I would say to drop the exhaust off the manifolds but if they have never been touched they might break instead of come loose.

Husband just told me when the Jeep sits at an idle the check engine light flashes, when he steps on the gas pedal the check engine light is solid.

That is still misfiring, if there is an issue with the converter being even partially plugged it could cause that as the exhaust isn't getting out of the system and the cylinders misfire. I would pull the O2 sensors and see what it does.

I borrowed a code reader, P0300, P0301, P0302 came up. Misfires. Put all new plugs and coil on plugs on. Cleared the codes. Waited a few minutes. Put reader back on. Now it shows; P201 fuel injector 1 circuit open. What does that mean?

The code is likely the injector connector on cylinder one came loose while you were changing the plugs. They can be touchy if they haven't been moved in a long time. I would check that it's on the injector and if it is the wiring to it may have been moved.