I only get dry/flaky skin after something special happens to my skin (like needling, scraping or electro), so maybe you're applying too much pressure on the razor which might remove a few layers of cells. The skin might be trying to repair itself, hence the dryness.
I personally just wait a few days and it comes back to normal. No creams necessary.
Actually, why not put your coconut oil BEFORE shaving, so the razor slides better instead of ''scraping''? Or maybe shave in the shower with or without soap. Just a few ideas...
All of this is assuming the shaving is what causes your dry skin, but maybe it's the amount of damn creams or oils that you all seem to love putting on your faces that creates it. Sorry not sorry!