Flint is a variety of chert.
Pure chert is made of the compound Silica Dioxide, and it is usually formed via precipitation from sea water, or accumulation of Siliceous materials at the bottom of an ocean as residues of organisms with siliceous structures (shells) drop to the ocean bottom. The crystals of silica dioxide in chert are too small to be visible to the naked eye, as opposed to the large crystals of silica dioxide that make up the mineral quartz.
Flint is an impure form of chert, and is believed to form a bit differently than most other cherts. Geologists believe it forms as nodules in limestone that are created as siliceous materials fill voids in the surrounding limestone, through a process called diageneses.
In diagenesis, the various compounds in sedementary layers separate and combine and reform with other similar materials as the layer is compressed and metamorphosed.