My guess from everything that has been said is that there is no charging port on the cover. However, this should be pretty easy to fix after the fact if Amazon gets enough requests or if an aftermarket supplier thinks the market is big enough.
Just make a cable that is USB on one end and has a five pin adapter with some magnets on the other end. Then you could plug the cover through the five-pin adapter. Since this is how it gets power through the Kindle when the Kindle is charging, this should work with existing covers.
So, if you care about this I would send Amazon an email (is
kindle-feedback@amazon.com the correct address?). If they get enough requests they may add a cover charging cable.
p.s. I wonder how close the charging adapter for my Microsoft Surface Pro I is to working? Even if it fits physically I suspect it puts out the wrong power (amperage?) for the Oasis. Here is a picture of the Surface plug.