I can't say if they would flavor the eggs, but I have sage, oregano, rosemary, catnip, and thyme where the chickens can get to them. Other than an episode of them hiding eggs in the sage, they don't bother them at all. Just protect the herbs if they are young enough that they could be scratched out by the feathered landscapers looking for tasty invertebrates.
I've only heard that garlic and onions could affect egg flavor. But if it makes the eggs taste like garlic or onion, I'd consider that pre-seasoning!
I was wondering if rose petals could produce rose-scented eggs
My girls devour rose petals and I had a brainstorm of getting a cherry-egger and feeding it a diet rich in rose petals...I could then sell Rose-Scented eggs for $8 a piece!
All I know is that various spices can effect their eggs taste. I don't think that many herbs would mess up the taste of the egg too much, but the best way to find out is to try it out yourself.