Should the left and right slides be the same number.
Yes. Different slides in different carbs on the same engine is wrong.
not sure if the carburetors are a matched set.
They are not.
If you look in your bike's Triumph parts book at the "Amal Carburettor T120R" pages, it says "L930/67" and "R930/66":-
. "L" and "R" denote which side of the body the air screw (and throttle screw if fitted) is/are fitted;
. "9" denotes a 900-series body casting;
. "30" is the inside diameter of the main venturi through the body from atmosphere to engine;
. "66" and "67" denote the bike and model year Amal supplied the carbs for. Carb. in hand but not knowing the vehicle, you could contact Burlen (the current Amal licencee) with the 'slash number', they would tell you the carb's original spec in terms of jet sizes, slide cutaway, needle, etc. and the vehicle it was supplied for.
. The exceptions are L301 and corresponding R300. Amal supplied these direct to dealers with 'average settings'. The idea was the dealer could bolt it to any suitable engine and the engine could at least be started, then the dealer could fine tune the carb to the specific engine by changing anything of jets, slide, needle as necessary.
If you are not hung up on having the 'correct' numbers on the outside of the bodies, it might be possible to turn what the bike has already into a "matched set".
Fitted new stay up floats and aluminum Viton tipped float valves.
Before incurring more expense on Amal parts, it is likely wise to have particularly the bodies measured for wear, because the price of genuine Amal parts bought individually can rapidly exceed the cost of a complete new carb and, if the slide bore is worn badly, a new carb or reboring and sleeving the old one is necessary.
Measuring bore wear needs a bore gauge (and someone who knows how to work it) to do it properly, because most wear happens on the engine slide of the slide bore just above the main venturi - the engine sucks the slide against that part of the body. Knowing the wear there, the slide should be 0.4 mm smaller diameter; greater clearance and more air is sucked between body and slide, screwing up the mixture.
The engine would run on the left cylinder at idle but the right runs decent once out of the idle circuit. I swapped the slides now the right side starts but left side will not fire untill out of the idle circuit and backfires.
The problem might be fixed just by fitting both carbs with slides with the same cutaway. Or it might be one or both carbs' idle circuits is/are not completely clear. The pilot jet is the usual suspect but the two tiny holes in the bottom of the main venturi, one each slide of the slide land on the engine side of the carb must also be clear.
If a carb is heavily corroded, it can be wise to drill out the 'block' at the 'atmosphere' end of the fuel passage so you can be sure it is also completely clear. Drilling out the block must be done with thought, as you must be able to block it again after cleaning. I use M5 grub screws and drill out the original block with a 4 mm drill (because 4.2 mm is the tapping size for M5); In the US, 10-32 grub screws might be easier to find?
Left side seems to flood easily.
If this means the right side does not, the float is depressed by a roll pin protruding from the tickler button inside the carb body. You can grab the roll pin gently with pliers and extend it a little further.