The blood eagle was a technique used by the vikings to torture people. They would cut the victim open, remove the bottom two ribs, and pull the lungs out. As the victim breathed the lungs would flap and spray blood everywhere, the lungs looked like an eagle. Hence the name.
Is it possible to do this to people in DF?
Short answer: No. Like most specific alleged historical tortures, there is no support for it in DF. Dwarves, the only playable fortress civ in stock DF, are entirely opposed to torture for any reason (check the entity Ethics files), which probably influences the lack of suitable mechanics.
Longer: There are a number of problems with your post. To start with, there is significant question as to whether the practice is actually historical at all; there are several reasons to believe that most if not all reports are the result of either poetic license or later (mostly Christian) writers attempting to emphasize how primitive earlier times were. AFAIK all of accounts usually referred to were written at least three hundred years after the events that they claim to represent, generally by individuals in significantly different cultures.
Like horned helmets, this seems to be something that owes most of its memetic existence from a long series of poorly researched or simply made up fictional references; the practice, even if it ever was performed at all, would have been extremely rare.
Additionally, in the few accounts that seem like they *might* have some basis in history, the practice sees to be described in terms of sacrifice to a god, not as torture per se; a method to dedicate a kill and victory to Odin, for example. In DF terms, this sounds more like the sort of thing you would expect from a demon posing as a deity; although "torture" is one of the 130 possible spheres for a deity.
Finally, I'm not familiar with traditional descriptions matching yours. The usual focus in the allegedly historical accounts is on carving on the back; the "wings" are supposedly provided by the ribs, which are entirely cut away.