How can critical thinking improve writing skills?

Critical thinking could unearth more ideas related to a subject as your thinking takes another direction. You get more to write on different aspects of a subject with critical thinking.
Any kind of thinking will improve your writing! Thinking critically means stepping away from the emotions involved and looking at things in a more scientific manner. This can improve your writing skills because you don't have the problem of being too attached to one specific part of what you wrote. You will be able to edit your work better because you can think logically instead of emotionally. Also, thinking about things critically will help you to be more observant, and your observations always show up in your writing.
Critical thinking requires clarity, and clarity requires understanding of what you're writing about or what your argument is based on, and understanding leads to being more articulate, and being more articulate means that you're able to put your thoughts down in Words that are concise, easy to understand, and in sentences that flow together well and make for an easier read.