And how should the sentence be translated? "It's a beautiful green town"? "It's a beautifuly green town"? "It's a greenish beautiful town"?
みどり in this sentence is not an adjective ("green", "greenish"), but a noun meaning "greenery".
きれい is an adjective modifying the above noun.
The whole sentence reads then as "It is a town with beautiful greenery".
が in effect does not connect two adjectives, but a part of relative clause. Either みどりのきれい or みどりがきれい can be used here, see this question.