I have not worked on an Amal MkII, but just looking at them they are definitely simple, particularly if like a Mikuni VM34. Don't be intimidated by the carburetors. Pull and clean. It's not guessing, it's what should be done to rule out blocked fuel circuits, and is common troubleshooting technique.
Before taking the carburetors off, you should check to be sure plenty of fuel is getting into the fuel bowls. Unscrew that main jet access nut on the bottom of the fuel bowl with a small bowl/container under the carburetor and the pet cock off. Fuel should come out. With the container still in place open the pet cock, fuel should pour out at that point. Close the pet cock. If fuel does not pour out of the bottom of the float bowl, you'll know there is an issue inside the float bowl or at the pet cock. Could be a couple of things preventing proper fuel flow, but I might be guessing and we can't have that. Anyway, you can address all of it with the carburetors off and on the bench.
I did not read any of the other replies, so if I repeated any wisdom my bad.