Q: Is it possible to chemically eradicate clover in a bed of dwarf iris?
A: My friend Theresa Schrum points out that irises are monocots (single-leafed plants) and therefore should be immune to 2,4-D, the primary ingredient in broadleaf (dicot) weedkillers. Many products containing 2,4-D are only labeled for lawn application. I suppose you could do a small test plot to see how the irises respond to a herbicide application.
Dr. Mark Czarnota has an excellent publication on other chemical options here: Weed Control in Iris.