I have a 1971 Ford Thunderbird With Cylinder Misfire Suggestions?
 

I tried everything including replace carburetor, distributor, plugs and wires to no avail. I took a video starting the engine with the misfire. Any suggestions what else may be causing it?

Welcome to the site..
How many miles on the car? Any engine work done etc?

Its not just the misfire,, but how hard it is to fire off that’s concerning.

Being you changed the plugs was the cylinder compression checked.? On any older engine, or whithout any document history it’s always good to know compression specs for checking ‘base engine’ health, more so for misfires and hard to start concerns . Listening to it crank over it ‘seems’ ok, but I’d want to know for sure what the comps are
..
Ignition timing is ? The reason for the question is,, even when it starts the throttle response is ‘very poor’ which some of the contributors are retarded timing (could be reading mechanically incorrect), vacuum advance isn’t working/or is missing vacuum supply, or the carb accelerator pump isn’t spraying fuel (if working, you shouldn’t need to feed it a fuel prime) and significant vacuum leaks.. Even though the carb is new, can you visibly see the accelerator pump applying a spray into the intake?
Its hard to detect or hear the misfire in the video,, but the hard to start condition is clear to see.
An engine with a cylinder not contributing, sometimes multiple cylinders will generally still yield a decent start with some throttle help, although a rough or unstable idle may be the result. The near totally flat throttle on a throttle snap or trying to rev it up is indicating to me, it’s more than just a misfire..

So in short,,,
Compression checked and is ?
Ignition timing is ? ( Could be reading wrong at the balancer, or incorrect valve timing is prior work done etc,) and is there a significant improvement if the timing is advanced?
Checked with a timing light, do you see the timing advance when the engine RPM is raised or on a throttle snap?
Verify the carbs accelerator pump is supplying a prime/spray (should be If new, but always check)
No major vacuum leaks (PCV, Carb base, Brake booster etc)
And of course correct firing orders for the plug/wires to cap.
The totally flat throttle response is a red flag......