Because it is hot, it could literally be anything - a hot electrical component that is heading towards failure when hot, carburation, wear in the carbs.BIKE DOESN'T LIKE HOT STARTS. IT TAKES 5 TO 10 KICKS TO GET IT GOING AND IDLE IS DIFFICULT.
Substitution testing might be the way forward but I strongly advise against early substitution of new carbs for old - very expensive if it is not the solution - the fault could be in any of many cheaper components.
If the engine is hot when you try to start it, be aware failing to start could be because the mixture is too rich - carbs heated by the hot engine while the bike is parked will cause more fuel to vaporise in them, this is exactly the same as tickling the carbs when the engine is cold; however, a hot engine does not require an extra rich mixture and might fail to ignite it.
Are the carbs fitted with air slides, aka "chokes"? If they are, I assume you are not deploying them when attempting any sort of hot start?
When starting - hot or cold - is the throttle closed or a little open? If you normally hold it a little open for a cold start, experiment with holding it open more for a hot start - if the current problem is an over-rich mixture because the carbs are hot, holding the throttle open more will admit more air and weaken the mixture.

I hope you do not open the throttle more as you kick? Useless with Amals.
If opening the throttle more before kicking does not reduce the number of kicks required to start when hot, try tickling the carbs before attempting a hot start? This might sound counter-productive but the new fuel into the carbs will cool them for a short period, then holding the throttle open more to draw in more air can produce a mixture the plugs can ignite.
Ime, if the engine has not started within five kicks, the mixture is either too rich or too weak.

If none of the above reduces the number of kicks required hot, I would start substitution testing with a new pair of spark plugs; however, unless the bike has thin-electrode plugs already, they are what I use - NGK B7EV, B7EVX or, if they are all you can get, B7EIX. Iirc your bike does not have electronic ignition? If not and it also does not have an electronic regulator/rectifier (instead of separate rectifier and Zener diode), try to avoid plugs with built-in resistors - BR...
Amals do not have an air jet. The air screw (horizontal on the engine side of the body) varies the amount of air admitted from the filter through the channel in the underside of the body because the pilot jet is a fixed orifice.adjusting the air jet
It is almost impossible to replace the pressed in pilot jet in a standard Amal Mk.1 Concentric.bigger pilot jet
In theory, it is possible to enlarge the orifice of the pressed in jet; however, in practice, as standard is 0.016" (16 thou) and the next size up is 0.018", the chances of enlarging it accurately are between remote and non existent. And, having enlarged it, if the original problem is not cured, it is impossible to reduce the size of the orifice again.