Millicenton was used almost exclusively in the "Saga of a Star World" and "Lost Planet of the Gods, Part I and Part II. If you consider that the early use of the centon in the pilot episode was something closer to a week, the millicenton would be somewhere in the neighborhood of ten minutes, or 1/1000 of a week.
In "Saga of a Star World", Jolly told Apollo that their landram would intersect with the Tylium mine in 24 millicentons (or roughly 2 hours). They were to check in with each other every four millicentons.
In "Lost Planet of the Gods, Part I", Adama told his guests that they had been "gorging ourselves on this delicious food for nigh on three millicentons, waiting" for Apollo's wedding proposal. Later, Starbuck told Apollo he was going to wait one millicenton before proceeding to enter the Void.
Millicenton made a belated appearance in "The Living Legend, Part II" when Sheba told the Gamoray landing team that "we've got millicentons to get in and out."
See also: Units of Measure (TOS)