He lists three books that helped him improve and clarify his writing: Stephen King's "On Writing: The Memoir of a Craft", Jon Winokur's "Advice to Writers", and William Zissner's "On Writing Well: The Classic Guide to Writing Nonfiction". The first two will likely be of limited relevance to science writers, unless they wish to make the jump into writing for the general public. "On Writing Well", however, seems promising, especially in the author's attitude towards "cluttered" writing. Along with outlining clear, concise rules for punctuation and grammar, William Zissner decries clutter as a "disease of American writing" and offers suggestions to improve writing that is "strangl[ed] in unnecessary words, circular constructions, pompous frills, and meaningless jargon". Sound like anything you know?
Obviously all of these books are directed towards native-English writers, and don't address the challenges inherent in writing in a second (or third, or fourth) language. If you feel fairly comfortable writing in English, these resources could supply some tools to help your prose feel more natural. In the end, academic writing is the same as any other kind of writing: communication with the reader is key. While scientists don't have the luxury of agonizing over every word the way a professional, full-time author might, I can't see the downside to taking small steps towards improving the overall quality of scientific publishing.