The answer to your question (of whether transferring once diminishes your chances of being accepted as a transfer into a UC) is no.
You’ll have to complete the necessary requirements for your major, and you’ll want to finish your general education requirements (either by IGETC if you plan to go to a community college, or by 7-course breadth, which can be tricky if you’ll be at a university which isn’t a UC.) But transferring once will not hurt your chances. You may want to briefly explain why you decided to leave your current institution in your application, but it’s not that big of a deal.