Taken from the Yamaha Flute Care and Maintenance Article.
After playing clean out using your cleaning rod and a polishing gauze. NEVER return your instrument after playing to its case without cleaning out first.
Sticking keys can be fixed (sometimes) by using "cleaning paper". Place the cleaning paper between the pad and the tone hole, press lightly a few times. If this doesn't clear the sticking, then take your instrument to a repairer for them to take a look.
A cheap alternative to "cleaning paper" is cigarette papers sometimes called Rizlas.
Periodically. clean your flute using a soft cloth. Taking care to remove dirt from around the mechanisms.
Periodically - at least once a year - get you flute serviced by a professional repairer.
NEVER place grease on either of the metal tendons on your instrument. Cork grease is ONLY for instruments with cork in the connecting parts, like a wooden flute or piccolo.