I don't know about the United States, but pretty much everywhere taking videos of airport security check is prohibited.
We don’t prohibit public, passengers or press from photographing, videotaping, or filming at screening locations. You can take pictures at our checkpoints as long as you’re not interfering with the screening process or slowing things down. We also ask that you do not film or take pictures of our monitors.
Missing context:
However… while the TSA does not prohibit photographs at screening locations, local laws, state statutes, or local ordinances might. Your best bet is to call ahead and see what that specific airport’s policy is.