It’s really hard to estimate travel time when moving to Chile, because there are so many factors.

I would first investigate international moving companies that could handle your job. Most of them should be able to give you an idea of how much your move will cost, and how long it will take for your items to get to Chile. Be sure you get an in-home moving estimate so they can see exactly what you need to have moved before you get final moving quotes.

As far as customs, I don’t believe it matters how long you’ve been in the U.S., but that's definitely something to discuss with your movers. 

Also, it's important to note that for an international move, the moving company must pack your items for you because they required to do a complete inventory and certify the contents of the shipment.  Most counties will not accept inventories prepared by the person who is moving -- the shipment will not pass customs.

As far as process, your goods will be transported to a port in the U.S., and then shipped to a Peruvian port. From there, your goods will be picked up by a Chilean mover and delivered to your residence in Santiago.