A word of warning about mirroring items: it’s really bad practice in Revit & BIM in general.
Why? Any given object might refer to a real-world item that is handed. Revit has no way of determining this, as there is no reliable way in Revit of determining the ‘true’ handedness of an object.
Thus you might be inadvertently creating an object that will cause big problems on site.
Not so important for a chair. Rather important (and very costly) for an MRI suite, and yes, I have seen this happen.
If you need to ‘turn something around’, then rotate 180 around z vector.
If you need to mirror something - well, there IS a flag you can set - use the API and RevitLookup to find it, but be warned that it is very inconsistent in its application and use. You’ll need to use some Python to enact it, the following code will attempt to identify Mirrored (Facing Flipped) elements.
#Copyright(c) 2014-2016, DanEDU Dynamo
#Erik Falck Jørgensen, Technical University of Denmark (DTU)
#Modified (butchered?) by Adrian Esdaile
#Inputs is stored in the IN variable
element = list(UnwrapElement(IN))
#check if element is FacingFlipped
list0 = 
list0 = [ (True if i.FacingFlipped else False) for i in element ]
#Assign output to the OUT variable
OUT = list0