It looks like a whole brisket to me, just a little thin. It's pretty well trimmed already so I wouldn't bother cutting away any more fat.
Really the cooking method is up to you. Some people trim the point from the flat and cook the flat to fork tenderness. The point is a lot fattier and you can leave that bad boy on there for a few hours after the flat is cooked. It'll give you some great burnt ends. Some people cook flats only....
I cook them whole. The flat section beside the point will remain a bit more moist than the far end of the flat. If you have people that like meat well done, serve that to them. Save the point portion for the flat for yourself.
You can always try and inject it before you cook it. It might add a bit of moisture to the thinnest part of the flat.
Otherwise it looks just like most briskets I've seen.