No, Brooklyn Bedding mattresses do not require a box spring, assuming there is some other kind of supportive foundation or bed support system.

Any type of support system that provides minimal to no flex will work with Brooklyn Bedding mattresses.
This includes most platform, slat, and box spring foundations. For slat foundations, check to make sure slats are no more than 3-4″ apart.
If you love the bed frame you have already, but it doesn’t provide support, consider adding a bunkie board. This is a thin piece of solid wood that provides support and prevents the mattress from sagging.
You can also look into low-profile boxsprings for the same support with only a 3-4″ height.