So simply put the problem I have is my bms turning off, or giving way less current/voltage (I don't have enough time to check) after I start driving the motor on the l298n. I could smell some burning, so my guess would be that the motor didn't have enough voltage to move, so it was basically just short circuiting, that's why I don't have time to check since I don't want to burn the motor. I tried connecting the motor directly to the output of the bms, but all that happens is the motor starts spinning for a slip second and then stops and short circuits again. I also tried connecting the motor directly to the output of the batteries and it works like it should, which means there is something the bms is doing that is either not letting enough current through or something similar. First I thought the over current protection was kicking in, but the bms I have (attached below) allows for a maximum current spike of 20A, and can handle 8A continuously (sounds a little high but even if it wasn't that high, there is no way the motor pulls anything close to that).
One thing I haven't tried is using the arduino to generate a lower pwn signal for the l298 so the motor pulls less current when starting, but again as I said the current shouldn't be a problem in my opinion.
If anyone has any experience with BMS', or knows about a better one I should get, I would appreciate it if you left a comment, thanks.
What is the stall current specification of the motor?
I'm not completely sure, since I took the motors I have out of an old toy, but it looks like one of those basic 3-6v motors, and I generally see them rated for around 0.4A. and something like 1.5-2A when they're stalled.
Can you post a data sheet for the BMS?
This is just a comment about the board. Or rather, a question. Why do they make those boards without mounting holes? Some holes for mounting (if needed) would be really nice.
I bought it from here.
I remembered that the problem could possibly be that the batteries can't provide enough power when everything is connected (I used a buck-boost converter between the bms and l298n to get the voltage I need for the motor). They are pretty old laptop cells so they could be pretty weak, although I didn't feel them heating up at all while connected.
There are two things written on the cells: "SE US18650GR" and "T G511JPL12".
After looking for a spec sheet, I found a few different sources saying different things, so I'm still not sure if they can discharge the needed amount, but I'm working on connecting them in a 2S2P pack to see if that helps, I'll post what I find out when I do it.
Southpark:
This is just a comment about the board. Or rather, a question. Why do they make those boards without mounting holes? Some holes for mounting (if needed) would be really nice.
Yeah that is pretty annoying, makes it harder to solder on the wires, and in general just less convenient to use 
Ok so I tried connecting in a 2S2P configuration and it seems like my problem after all was the batteries not being able to supply enough power.... kind of a bummer.
Does anyone live in europe and have any recommendations on 18650 suppliers with preferably low shipping? 
The L298 is a poor choice for a motor driver, nowadays, especially when you are running on batteries. That driver is ancient and very inefficient. It dissipates (wastes) 2 to over 4 volts of the motor power as heat. Pololu has a good line of modern motor drivers that are much more efficient. The drivers are available from many vendors, but Pololu has instructional pages for each of its drivers that show how to use the drivers properly. A better driver will help with your power problem.
You need to determine the stall current for the motor to be able to pick a driver. To estimate the stall current, measure the motor winding resistance. Take several measurements rotating the motor a bit between readings. Use the lowest reading in the calculation. The estimated stall current is the motor supply voltage divided by the measured resistance.
Thanks for the tip, they do seem like they would be more fitting, but they are a little pricey, and since this is for a school project I don't want to spend additional money on parts.
Maybe one day I'll look into the Pololu motor drivers a little more.