What could cause a flame sensor to stop working so frequently?
Have you had a gas technician go over your entire combustion system?

I strongly suspect that something is not adjusted correctly, and you have excess soot production (lint seems like a red herring, frankly) which is making the sensor "dirty." It also means you are not burning your gas as efficiently as should be possible. This is almost certainly a problem with combustion, not the sensor. The sensor fouling is a symptom, not a cause.

I don't really regard this a great area for DIY - without the right tools, which cost more than most homeowners (including me) will spend, and the right training to go with them, screwing up combustion appliances though self-service is more common than tuning them perfectly. There's also "not creating a giant loophole for your insurance company if the house burns down" as a minor factor in that thinking. Having burners professionally serviced on a yearly basis is a minor expense, comparatively.

If (as is commonly the case with high-efficency burners) the furnace has both an air intake from and an exhaust to outside, the dryer lint really can't be the problem. Some sort of blockage of that intake could, however, potentially cause the problem you are having (insufficient air supply causing a rich, sooty flame; soot fouling the sensor.)