It takes up to 30-45 days for a military care package to get to Europe or Korea.
(From Department of the Army Postal Program)
Listed transit times are measured from the local post office (Anywhere, USA) to arrival at a military postal unit overseas. This transit time includes three to four days to go from the local post office to the U. S. Postal Service "gateway" (Chicago, New York or San Francisco). Parcel post, however, can take 7 to 10 days to reach the gateways. At the gateway mail is sorted, bagged, and tagged to arrive at a military postal unit overseas. While commercial aircraft are very consistent, there could be a large variation in transit times due to military aircraft schedules, weather, transportation and military operations in theater, or movement of a Service member's unit.
Military mail moves using USPS transportation network while in the United States until it arrives at one of the major processing center either on the east or west coast. All First-Class, Priority, or Express mail will move to the major stateside gate way to an oversee gateway via commercial US owned aircraft. Once Mail arrives are overseas gateways mail is distributed to designated post offices for the delivery to individuals. Mail posted as Standard postage rate will move using USPS while in the states and the transition to US seaport to overseas seaport. Standard posted mail will be distributed using various means to designated post offices and then individual.