Can a marble floor be flamed like a granite floor?

No. Most marble, with the exception of certain limestones, cannot be flamed. The mineral make up of marble will not allow the surface to become flamed. Trying to do so will only burn the surface.

FYI If you come across an unknown stone surface and it appears to have a flamed surface, this should be a big hint that it is not marble. As mentioned above there are some limestones that can be flamed. Some German and French limestones can accept a flamed finish.