Cover Crop Flexibility Act of 2021 This bill modifies the federal crop insurance program to address the planting of cover crops following prevented planting. Specifically, the bill allows a producer that is prevented from planting its first crop to plant a second crop and receive an indemnity equal to the full guarantee for the first crop if the second crop (1) is an approved cover crop, and (2) cannot be harvested for grain or other uses unrelated to livestock forage or conservation. Under current law, if a producer plants a second crop it can only get an indemnity worth at most 35% of the prevented planting guarantee for the first crop. For a producer planting a cover crop following prevented planting, the Federal Crop Insurance Corporation (FCIC) may provide separate prevented planting coverage factors that include preplanting costs and the cost of cover crop seed. Further, the FCIC must conduct research and development regarding a policy to insure crops on fields that regularly utilize cover crops, including research to examine the extent that cover crops reduce risks of prevented planting and other crop insurance losses.