an advanced degree (MA, MS, PhD) from US and UK universities
I'm sure there is a relationship between higher levels of education and better academic writing in a very general sense. However, I think it's overemphasized. The more important indicator is probably the bachelor's degree, as that's the point where you can assume the writer has at least basic abilities. But more on this in a moment.
If i were advising a student on finding a good writer, I would tell the student not to be assured by the letters MA, MS, or PhD after a name. I have seen some papers produced by U.S.-born advanced-degree holders that were purely wretched.
You have to consider: Someone with an advanced degree will have written several graduate-level papers and probably one thesis or dissertation. An experienced professional, no matter the education level, will have written thousands of papers and dozens of theses/dissertations. Who's going to know the keys to success?
In truth, the percentage of people you can trust to produce a decent paper is very low, no matter if they have a bachelor's, master's, or doctorate; no matter if they come from the same country as you; and no matter if they share your major. The people you can trust are those with extensive practice with academic writing conventions and enough experience to have previously come across the kind of assignment you're dealing with. In other words, you can trust the people who do this every day and seem to be making a living. There is a loose relationship with education level and a tight relationship with aptitude and experience. Academic writing is a style and a practice, and one that some people, by nature, pick up much more readily than others.
All other things being equal, a graduate degree is an advantage, especially for graduate-level work. However, advanced degrees are something that many ESL writers and domestic hacks use as a marketing tool, a proxy for being a good academic writer. They are not a substitute for actually being a good academic writer.
The standard advice holds: When you find a seemingly legitimate and capable writer or company, place a small order and see how it goes. This test will tell you much more than a resume or CV ever could. If it works out, start placing larger orders.