Is it permissible to marry the daughter of the paternal cousin whose grandmother breastfed the questioner's grandmother, knowing that the questioner also breastfed from his grandmother but her breast had no milk?

Lactation is only established with certainty of the milk separating from the breast and reaching the inside of the infant's stomach. If your grandmother had no milk and there is no certainty that milk separated from her and entered your stomach, then it is not considered lactation. Therefore, you may marry your maternal aunt's granddaughter. You should clarify to the girl's family that the lactation is not established and that the lactation which prohibits marriage must consist of five full, satisfying sucklings.