You need to replace the rubber seals in both the master cylinder and the caliper. Doesn’t matter how much you bleed if those are old you wont have strong brakes.
If the kart is from the early 2000s or earlier they used MCP brakes. Margay I think still uses them and I’ve seen the parts on Comet kart sales before.
Maybe sand the pads if the seem glazed. Make sure the linkage is on the highest hole on the master cylinder and the lowest hole on the pedal. Assuming they have multiple holes this will give you the most leverage.