Is it permissible for me to meet my paternal uncle's brother through rada'a (nursing)?

No, a state of mahramiyyah (unmarriageability due to close kinship) is not established between you and this man, because he is your uncle's brother through rada'ah (milk-kinship), unless he was nursed by one of your direct ascendants. You are a ghair mahram (marriageable non-relative) to him, so it is not permissible for you to interact with him as you would with your mahrams, in terms of looking, privacy (khalwah), and similar matters.