You wouldn't like your wooden nose flutes to dry in the time, and have some slits appearing in the assemblings. Nor would you like them to become grey with repeted handlings. The best way is to protect them from crud and feed the wood to keep it up at its best.
For this, I use Lemon Oil (in fact : lemontree oil). It is primarily dedicated to the maintenance of guitars and other neck instruments fretboards, and can be bought in any music instrument shop.
One may use other oils, but some become rancid with time (olive oil for instance). More, the lemon oil lets a nice soft lemon aroma on your flute.
The operations are quite simple : cover the nose flute with a generous coat of oil wherever you can, wipe the excess with a paper towel, and use this excess to access the places and crannies that weren't accessible with the oil bottle cotton pad. Then, let the wood absorb the oil during several hours. Done for 6 months!
Warning : some woods may darken a little bit with this treatment, others don't.
Here with a Heinrich Handler's nose flute :