“The explanations I’ve heard is that Noah did not take the “unclean” animals on the Ark with him.”
That’s incorrect, the Bible clearly states that he took both clean and unclean animals aboard the Ark. He just took fewer of the unclean ones. So anyone making that argument is probably not very well informed.
“What other theories do that have to explain the extinction of all the plants and animals that we find only in the fossil record?”
Personally, I think there was a radical change in the environment during the time of the flood, and that many species simply could not adapt. For example, many of the creatures we see that are extinct could not have survived at our current atmospheric pressure. If the pressure was higher before the flood, then dropped afterwards, any species above a certain size would have died very quickly, unless they were completely aquatic, like whales.
There's not shortage of examples of small animals and fish in the fossil records, not to mention plants. What evidence do you have that this is what happened?
Whatever changes occurred would have to be lethal to a wide variety of birds, land and aquatic animals, and plants, except for people and the modern animals we see today. Whatever conditions existed before that had to be suitable to all of them.