If the battery is only meant to put out 15A, then upgrading the BMS is not a good idea--a BMS is sized to protect the cells against damage, so if it's at 15A it should mean that the cells are only capable of that. Using them at higher rates could damage them, which could lead to a fire.
As for "calculating" current, you'd need to actually measure the current to know what's happening. Or measure hte voltage and the wattage at the same moment of highest load, and use that to calculate the current.
You don't specify how you calculated it or what information was used to do so or under what conditions that informaiton was gathered, so we can't tell you fi tha't rigfht or not.
Besides, if he wants faster, increasing current doesn't do that--that increases torque. Increasing voltage increases speed. The increased speed may also require higher power to do this job, and higher current may be a part of that, but higher voltage is the first stage.
So you'd need a new battery that has sufficient voltage to get the speed you need with the wheel and mtoor you have. It's directly proportional, so whatever the max speed you get now, take the new speed and divide it by the old speed. Use that number and multiply your present voltage by that, whcih gives you the minimum new voltage required.
The battery also has to be able to supply the current required to get the total power needed to go the faster speed under the riding conditions you have.
Additionally, the controller (and display, etc) have to be designed to handle that higher voltage; if they're not you'll need new ones.