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C=O and C=C bonds cannot be chiral.In your molecule there seem to be 4 chiral centers.Simply put the same criteria apply for simple and complex molecules, 4 different substituents and non-superimposable on it's mirror image.
There are not 4 different substituents on that carbon atom. It's part of a phenyl ring. The double bonds are not static as you said.
Well assuming you could brominate there then it would give a new chiral centre.
So, then these four carbons would be the chiral centers (marked with red stars)?In that case, we have 16 stereoisomers (2^n) and 14 diasteroisomers (2^n - 2), correct?