Marrying a maternal cousin although his brothers suckled with his maternal uncles
If the reality is as you have mentioned, i.e.
Your maternal uncles and your elder brothers were breastfed by your mother and grandmother, if they were so breastfed by both your mother and grandmother five times or more during their first two years, it is not permissible for you to marry any of the daughters of these maternal uncles because you became their paternal uncle (the brother of their fathers) through breastfeeding. On the other hand, if they were breastfed less than this number or at any other time than their first two years, it is permissible for you to marry any of (Part No. 21; Page No. 122) the daughters of those who were so breastfed. Allah (Exalted be He) says:
Forbidden to you (for marriage) are: your mothers
...your brother’s daughters, your sister’s daughters
The mothers shall give suck to their children for two whole years, (that is) for those (parents) who desire to complete the term of suckling
It was proven that the Prophet (peace be upon him) said:
Milk relationships are equal to blood relationships in rendering marriage unlawful, i.e. whatever is prohibited due to blood relationships is also prohibited by milk relationships.
It was also authentically reported that
`Aishah (may Allah be pleased with her) said:
"It was among the revelation of the Qur'an that ten known times of breastfeeding make the marriage prohibited, but this was later abrogated and reduced to five. The Messenger of Allah (peace be upon him) died and the ruling remained effective."
It is worth mentioning that if a baby sucks milk from the breast, no matter how little is it, and then leaves it, this will be counted as one suckling. If it sucks milk again from the breast, no matter how little is it, and then leaves it, this will be counted as a second suckling, etc.As for your maternal uncle's daughter mentioned in your question, she is marriageable to you, because she was breastfed by neither your mother nor your grandmother, and you were neither breastfed by her mother nor her grandmother, as you have mentioned in your question. (Part No. 21; Page No. 123) May Allah grant us success. May peace and blessings be upon our Prophet Muhammad, his family, and Companions.