For the question: “how many calories do you burn licking an envelope”, there are two competing factors to consider. On the one hand you burn calories through the licking action, but on the other hand you consume calories by absorbing the liquid adhesive. The question then becomes: which is stronger, and so is there a net effect?
The glue used to seal envelopes is sweetened by a substance known as Gum Arabic, Acacia, Sedan or E414, which is found in many popular candy bars and is derived from tree sap. The FDA has officially recognized the substance as containing 1.7 calories (kcal) per gram.
As a ballpark estimate, we can say that any given envelope is coated with approximately one hundredth of a gram of glue, which in turn consists of about 10% E414. We will further postulate that the calorific content of the glue is to a good approximation due entirely to the E414 additive. Therefore, one envelope contains about one thousandth of a gram of E414, which accounts for 0.0017 calories.
We can further estimate that the action of lifting an envelope to your face and licking it burns about 10 calories per hour. It takes about 1 second to complete the motion once, and so you can expect to burn about 0.17 calories per envelope lick. We can see that this is 100 times greater than the estimate above for the calorie content of a single stamp.
Going by this estimation, it would seem that the calorie intake of an envelope is actually negative, in that you burn more calories through the action of licking it than you gain through absorbing the glue substance. All of the above is of course a rough estimate, but even if the guesswork is out by a factor of 100 it doesn’t seem as if you will get fat by licking stamps.