All perfect praise be to Allah, The Lord of the Worlds. I testify that there is none worthy of worship except Allah, and that Muhammad is His slave and Messenger.
The breastfeeding relationship is not confirmed by suckling milk from the same cow or the same goat, regardless of the kind of milk that is produced from them. The breastfeeding that makes a person prohibited for marriage is suckling from (the same) woman.
Shaykh Ibn 'Uthaymeen said: “His saying: ‘Its opposite is the animal’; means that the milk of an animal does not make the persons who breastfed from it forbidden from marrying each other. If we presume that two children suckled milk from the same animal, and each one of the two breastfed five times, do they become siblings by means of breastfeeding? The answer is no; otherwise, all the members of the family will become brothers by means breastfeeding if they drink the milk of the same cow. So, we conclude from this that it is a condition that the (suckled) milk must be from a female human (woman). Naturally, the term ‘female human’ excludes animals.” [End of quote]
For more benefit, please refer to Fatwa 363460.
Allah knows best.