Suppose I have two vectors: an empty lenti destination vector, and the same vector with a FLAG-tagged protein X cloned in. Does it make sense to perform ChIP using a FLAG ab on both samples? What does that accomplish for my empty vector samples, besides non-specific "ab to chromatin binding"? If anything, the empty vector would serve as a lenti control, in the rare event that introducing a lenti vector would cause protein X to bind to chromatin. In that case, a FLAG ab wouldn't help as the vector doesn't code for FLAG; I would need to use an ab for protein X to really assess that.
FLAG is so artificial that it would be unreasonable to find endogenous levels in the vector control samples. Wouldn't it make more sense to use an ab to the native protein for ChIP (presuming one is available), then one could compare between endogenous/basal levels and exogenous/over-expressed levels?