I received a 1099-MISC from a publisher for royalties. However, I also received a 1099-K from Paypal listing the same payments. How do I avoid getting double taxed?

I understand your concern, but there is really no way to report both of them. Just report the income once from the 1099-MISC and do not be concerned with the 1099-K. Keep it for your records with a note, so you have documentation.