And here’s a really solid discussion of the sugya: sorry link removed
Agav, there are several interesting points about this discussion: (1) In his opinion, a ideally a bris milah should davka real meat, and not just chicken. (2) He concludes that lma’aseh it’s fine to have a milchig bris. (3) He quotes the tshuvose chasam sofer (OC 69) who states kdavar pashut that one can make a milchig bris, and even on shabbos.