F-16s are not going to help. They need state-of-the-art F-35 stealth multirole fighters if they want to have a chance.
The US has more than 700 F-35s, and the Ukrainians need to have access to as many of them as possible for a coordinated strike to stand a chance against Russia.
If the Patriots failed to shoot down Scuds designed in the 1950s, no way in hell they’re ever going to intercept a Kinzhal:
Intercepting a missile is not the same as an airplane that flies at a much slower speed and a much larger target.