Do records show that thousands of flights are being canceled as vaccinated pilots fall ill or die?

There's no evidence that's happening. The claim in a published article is made without offering proof that pilots who have been vaccinated are either getting sick or dying, forcing cancellations.

The article making the claim misstates research into incidence of thromboembolism among pilots and also repeats the false claim that four British Airways pilots who received the COVID-19 vaccine died in one week.

A spokesperson for the Air Line Pilots Association, in an email to Lead Stories, disputed the "thousands of flights canceled" claim, writing :

"Pilots are healthy and the vaccine is keeping us healthier, even in the midst of the pandemic."

Online research on flight cancellations due to pilot illness and death from COVID-19 found no other published news reports regarding the claim.