Licking your elbow is one of those things that you "can't do". Whenever I hear people say this I love proving them wrong (even if it does look a little silly).
I'm not making any guarantees here, but I think a lot more people are capable of licking their elbows if they use the proper technique and have decent flexibility.
First you need to take your dominant arm and fold it up so your forearm is pressed against your bicep. Lift up your elbow so it is roughly at mouth level. Take the opposite hand and grasp the arm around the elbow, but make sure the actual tip of the elbow (target to be licked) is still accessible. Push your dominant arm back (think of it as pushing your shoulder back) to minimize distance from elbow to head. If you did this correctly your elbow should be just out of reach from your tongue. To close the remaining distance twist your dominant arm outward so your hand is to the side of your shoulder. Crane your neck forward and press your chin against your dominant forearm as close to the elbow as possible. Stick out your tongue and lick. With a bit of minor adjustment you should be able to touch the tip of your tongue to the tip of your elbow.
The only real use for this "skill" is showing off; try telling people you bet they can't lick their elbow, make them attempt it and of course fail and when they are convinced this also means you can't lick your elbow prove them wrong. You could also of course lick food off your elbow if no napkins are available but I have no idea how food would get there in the first place.