The Jack Hot scooter has a very difficult charger plug to test because its terminals are so small and close together. To test the charger we would remove the charger port from the scooter, unplug it from the battery, and then plug the charger into the charger port and wall and test for Voltage at the charger port's red battery connector.
Once the charger port is removed from the scooter it could be tested by sticking an appropriate size wire in the port terminals and testing for continuity between the terminals at the red connector.
The DC Volts setting would be used on the meter. Most multimeters have a 200 Volt DC setting which would be a good one to use. There is no risk of getting shocked because the charger output Voltage is too low for shocks. You should be able to gently push the probes (sticks) into the back of the connector where the wires enter into it to read the Voltage.
Faulty parts on electric scooters usually cannot be properly diagnosed without testing. You could try replacing the battery management system and see if that solves the problem. We would test the charger and charger port first though to make sure they are working.