A quick check using the "vlax" functions in AutoLISP verified that the Rotation property is exposed in the API. I have gotten a little rusty on the specifics of accessing data from the drawing in a Formula Property, but after a few searches of this blog, I had enough to refresh my memory and come up with this as the formula for a Formula Property in a Property Set Definition that applies to Multi-View Block References:
pi = 3.141592653589793238462643383
Set acadApp = GetObject(,"AutoCAD.Application")
Set mvbObj = acadApp.ActiveDocument.ObjectIDToObject( [ObjectID] )
RESULT = CDbl(mvbObj.Rotation * 180.0 / pi)
Before you create the Formula Property, add an instance of the ObjectID automatic property to the same Property Set Definition. In the formula, [ObjectID] needs to be a reference to that property, created by double clicking on the property in the Insert Property Definitions area of the Formula Property Definition dialog. You cannot just type [ObjectID] in the formula. When the reference is added, it will have a light gray background.
The angle value obtained from the Multi-View Block Reference object is in radians; I chose to convert that value to degrees. If radians will suit your needs better, you can delete the first line and, in the RESULT line, delete * 180.0 / pi. After posting my reply, I came across a better way to generate the value for pi:
pi = 4 * Atn( 1.0 )