While it may look rough, that film flaking off your lenses doesn't mean your glasses have reached the end of the line – most likely it's simply the anti-reflective coating that's peeling away. Intact AR coating reduces glare and lets your peepers shine through more clearly, but a peeling anti-glare coat impairs both your sight and your style. You can remedy the issue with a bit of sunscreen, though it means losing the coating for good. Consider this a last-ditch solution before having to spring for new eyewear.
Run your lenses under warm water, rubbing them with the pads of your fingers and a small drop of mild dish detergent. Rinse the lenses free of soap and dry them with a soft and clean cotton or microfiber cloth.
Apply a dab of sunscreen to another clean cotton rag. Due to its aluminum content, an oil-free SPF 45 variety does the trick here – the aluminum powder is just abrasive enough to remove the coating, but not rough enough to scratch the lenses.
Polish the lenses with the sunscreen lotion. Apply moderate pressure and work in a circular motion. You'll need to polish both sides of each lens, so focus on one side at a time, buffing the lens until the coating becomes patchy and flakes even more. Continue buffing until each side of each lens feels completely smooth. Rinse the lenses with plain water and re-apply the sunscreen to the rag as necessary.
Repeat the initial cleaning and drying process once your lenses feel totally smooth and are visibly free of any flaking or peeling.
To prevent your anti-reflective coating from peeling or scratching in the first place, use only lens cleaners specially formulated for coated lenses. Always use a damp cloth to clean the lenses, as a dry cloth may lead to marks or flaking.