I wonder about the truth of what is fed changing the flavor. Or maybe you'd need to feed really a lot of whatever had the flavor. Last year we raised chicks without using commercial chick starter and so were looking for ways to offer varied diet and plenty of protein. One thing we fed was minnows scooped out of our pond. When the pullets started laying the eggs didn't taste fishy which I've heard can happen.
Same with our goats and milk taste. We feed garlic scapes or chives for their help with worms and the milk has never tasted of these--nor of the thyme and oregano we sometimes feed for the same purpose.
Our rabbits get various herbs in their buckets of forage all through the growing season. I also use herbs to flavor rabbit when I'm cooking but I don't think the herbs they're fed flavor the meat. (We don't feed pellets so all the rabbit I've ever eaten was raised on natural feed, lots of forage. Whether that meat tastes different from meat of pellet fed rabbits I just don't know.
