It was hard to find information about what they do actually, but I found some information in this article on their blog:
Instead of using lithium or cobalt, Flint’s battery uses zinc and manganese—two of the most abundant and sustainable metals on Earth. And the core of the battery? It’s made of cellulose paper, which is biodegradable.
So this is a Zn-Mn battery, they just use a cellulose based electrolyte. If you search for "Zinc Manganese" you will find a lot of research papers from the last couple of years.
The conclusion of one of the papers:
The second [challenge] is to increase the areal capacity of cathode materials. Recently reported doped MnxOy cathodes only demonstrated an areal capacity of 0.1–0.2 mAh cm^−2^ due to the relatively low mass loading, which is far below the commercial standard (>2 mAh cm^−2^).
So it's energy density should be an order of magnitude lower than current battery technology.
It doesn't sound as revolutionary, but a step in a good direction.