How do I repair a flaking finish on my wood windows?
I can't quite tell from the pictures, but I suspect that you're describing the varnish (urethane) that's used to protect the windows. It does degrade over time from UV exposure, and will need to be re-applied (after sanding). This also applies to wooden outdoor furniture, which is where I've seen similar "flaking."

HOWEVER, the wood in your bottom picture shows a suspicious discoloration that looks like water damage, and this may mean a far bigger problem (it might also be what's broken the bond between wood and varnish). It could be as simple as water that is pooling on the window sill and finding a way into the wood (weather-related expansion can open cracks in the joints). Or it could indicate that water is being wicked into the wood from the foundation, or even via the sill.

If there is water damage and you can't easily determine the cause, I'd suggest calling a local contractor to take a closer look.