Flicker in the Capture, LED light source
Here is a blog posting from one of the leading LED fixture manufacturers, SORAA.  (Their chief scientist won the Nobel Prize for the invention of the blue LED.)  One of the design problems is that a rippler-suppressor reduces LED output efficiency by 2%-3%.  If you are a consumer looking for absolute Lumens from a given form factor, or highest Lumens per Watt, you'll end up buying a product that compromises on flicker in favor of output.  Moreover, while the industry used to agree on a definition of a flicker index, they are walking away from that and going to very application (and person)-specific definitions.  In the referenced article, mention was made that in the state of California, the only recognized flicker test is performed by the person sensitive to the phenomenon.  Finally, if you are using these lights for anything other than scientific motion studies, i.e., if color is actually important to you, Color Rendering Index (CRI) may also be important.

Obviously, cameras have very different sensitivity than humans.  And specialty instruments (made for high-speed video) exist, with more expensive power supplies and lower lumen/watt output.  I have been impressed with the SORAA lights I've purchased (CRI 95, and no visible flicker at framerates I've used).  If they don't test out for you, the best alternative is to get a specialty light that does specifically advertise flicker-free (usually by using a true DC power supply).