It wouldn’t be fleishig, it would be assur.
There is a halachah not to bake milchig or fleishig “pas” which actually includes cookies, cakes, and pies.
There are ways to do it that would be muttar (special shape or baking only enough for that day), but then you would have to tell them; you couldn’t just say it was a fleshig dish because they wouldn’t know to wait six hours.
It would be pretty difficult to put meat in without affecting the taste…