To expand on the "wet sponge / cloth / finger concept":
As we are dealing with multiple envelopes, I recommend layering the flaps of the envelopes, slightly staggered, so that the sticky parts of the flap form a coherent area, looking somewhat like '>>>>'.
Then use your preferred method of moistening (I recommend a damp sponge) to wet all the seals in one go and close one envelope after another.
Instead of folding down each flap, I recommend you grab the envelope at the rectangular part, pull it away from the rest of the sticky pile and fold it up towards the flap, so that the front of the envelope is on top again. It's one smooth movement without the risk of paper cuts (edge of the flap!) or sticky fingers.
(Source: Helping with business mass mailings as kid.)