Well, you don't match the motor to the battery, you match the battery to the motor and controller, so you're going about this backwards.
Before you go any further, you should look up and read the various Kart threads here on ES, to see what others have done that is similar to what you want to do, and then you can just do what they did if you like the easy way. One possible list:
https://endless-sphere.com/forums/search.php?keywords=kart*&terms=all&author=&sc=1&sf=titleonly&sr=topics&sk=t&sd=d&st=0&ch=300&t=0&submit=Search
If you prefer the hard way, then:
First you need to determine how much motor it will take to make the kart perform the way you want. If you're using a non-hub motor (chain drive/etc) then you pick the motor that will give you the watts you need both peak and continuous, and then can provide either the torque or the RPM needed for the acceleration or the speed you are after, at the system voltage you want to use. Then you can change the gearing ratio between motor and wheel to increase torque/decrease RPM, or vice-versa, as needed, to make the system do what you want. You can go to http://ebikes.ca/simulator and read the whole page, then play with the simulator, to learn how voltage, current, watts, torque, riding conditions, etc., all interact with the motor to give you your desired result. It'll take a while to figure out what's being shown to you, but it is a huge help in understanding what's going on in a system, and will help you more than any other single tool, to get what you want out of a system (even if you don't use any of the actual parts simulated there).
Then you pick a controller that can provide the current needed to make the motor produce the watts needed, at the system voltage you want to use. (volts x current = watts)
*Then* you pick a battery that can supply the current the controller needs to do that. If the battery cannot output sufficient current, then voltage will sag and total power output will be insufficient, and the battery will get hot (bad for battery, if it's hot enough it can catch fire). If the battery has a BMS, the BMS has to be able to handle the peak and continuous current the controller needs, too, but at least it should be able to protect the cells of the battery from overcurrent (if you use a BMS that is rated for what the battery can handle...if you use a BMS that's too big, it can't protect the battery).
