The Talmud (Yoma 75a) quotes two opinions: either the man could taste like everything except 5 flavors but never changed its texture, or the man could change its texture to anything but 5 things but it could still taste like those 5 without changing texture. The 5 things are those mentioned in the pasuk in Bamidbar 11:5: Kishuim Avatichim Chatzir Betzalim and Shumim (I don't know if these are actually their modern Hebrew equivalents, but if they are then they are all vegetables).
Your question is only according to the latter opinion.
I think the man could not become meat for two reasons. First, if the man could turn into meat, why did the Jews complain about not having meat? We see they did complain about the lack of these five things. Additionally, they complain in the pasuk above about a sixth thing, fish, yet the talmud does not record fish among the exceptions to tastes. Thus it seems that it could not taste like fish, but that was no cause to be an exception, implying a more general and known excluded category, likely meat.
So there was no way to have meat and milk man.
Furthermore, even if there would be, I submit that it would be muttar. The mishna in Chullin explicitly excludes fowl (and according to some non-normative opinions even undomesticated animals) from the prohibition of meat and milk as they are not similar to the 'gedi' (goat) mentioned as the prototype in the pasuk. It seems to me that all opinions would agree to exclude man as it is at best a 'plant'.
Finally I would like to echo avi's sentiment in the comments above, that the pasuk tells us explicitly in Bamidbar 11:8 that the man tasted like "cake baked with oil". Yum!