with 14hp the engine should have enough torque to move a light to midweight kart on 18" wheels... with an overall ratio of almost 7:1
BUT only at it's high torque rpm.
a centrifugal clutch takes care of that for you.. it engages around that rpms
and thus the kart will take off.
with a belt clutch you'll be the one who needs to set rpm, and not just any.
should be about 2000 - 2600 for good torque I guess (not knowing the engine, but assuming some industrial/mower engine is used)
bad news is, at 2000 rpm the belt travels at quite some speed already (at ~27mph)
so it's perfectly normal that it'll slip at first (that's your horrible squeaking noise)
so with a belt clutch I'm afraid you need to gear as you would a much smaller engine,
to get to a point where about half of that rpm is capable of accelerating your kart.
(and that'll make it very slow in the end)
it's all mower parts I assume?
mower engine and belts.. mower wheels, right?
basically the former top speed of the mower is what you need to gear for -a tiny bit more-
in order to make the belt clutch reliable (and silent

)
'sid