What is the value of a double etched penny with both Lincoln and Kennedy on it?

Coins are not etched, they are struck or minted. Etching uses acid to dissolve metal or another substance from on top of a substrate. Unfortunately they have no numismatic value other than 1 cent. Some novelty-item collectors will pay a premium for one that's still attached to its original packaging.

These "Lincoln Facing Kennedy" pennies were made by private companies -- mostly in the 1970's -- that took a normal penny and stamped a portrait of President Kennedy facing President Lincoln on the front of the coin. They were normally attached to some kind of card that listed the "Astonishing Coincidences" between the two presidents. The card was usually stamped with a company name & address, and they were often given out as an advertising gimmick by small businesses to attract customers.

Note that some of the "amazing coincidences" require stretching history quite a bit.