It is permissible for this young man to propose to the girl mentioned, because there is no impediment to doing so. The fact that his brother was breastfed with the girl's maternal uncle does not have any ramifications, not even with her sisters if there are any. The prohibition affects the one who was breastfed (which in this case is his brother) and anyone else who was breastfed by the same woman.
The young man mentioned here is not one of these people.
With regard to the older brother, if he was breastfed by the grandmother of the girl, then he is a maternal uncle to her through breastfeeding.
And Allah knows best.
Reproduced from Islam QA