Here is their white paper.
https://brain.fm/assets/pdfs/new_white_paper_unformatted.pdf
This appears to be the extent of their claim:
"Behavioral results suggested this music did help people over time, but the differences in the brain appeared first, were easier to see, and verified that the experimental manipulation (added modulation) was having a measurable impact on brain activity beyond auditory cortex"
Continuing down the rabbit hole, here is their grant application:
https://www.nsf.gov/awardsearch/showAward?AWD_ID=1720698
They are pursuing publication of a paper, but I can't find anything about it beyond what is on their website.
Also found this other FAQ paper:
https://www1.brain.fm/assets/pdfs/science_FAQ.pdf
They claim their music can improve slow-wave sleep, although this study looked at just three subjects