Having a brake bleed kit helps do the job quickly and cleanly, but if you're not doing it very often you don't necessarily need a kit.
As long as your bike is setup so there aren't many places for bubbles to get caught, you can just work the lever and tap the lines and so on while the bleed bolts are open, to assist air bubbles rising to the top and out of the system (catching any leaking fluid in a perfectly clean container so you can re-use it).
I have a bleed kit and don't bother using it, my bike generally doesn't trap any air bubbles anyway.
If there are a few small bubbles in the system, the brake lever will still work, it'll just feel a tad spongy or soft. I would just try doing as good a job as you can without a bleed kit, and then if they aren't working as good as they should order a proper kit for your Promax brakes.