Anyone can teach creative writing. You don't need special qualifications to set yourself up as a teacher, you just have to do it - or persuade someone to employ you as a teacher. Nor do you need special qualifications to set yourself up as a book doctor, or editor. All you have to do is persuade somebody to pay you to read/edit their manuscript.
So, if you're looking for a creative writing class, what should you look for in a teacher? In my opinion they should have at least one of the following three areas.
Just because a writer has been published it doesn't make them any good as a teacher. However, they will at least have some first hand 'how to' knowledge, both of how to write and how to get published. Does it matter what they've published? For myself, I'm published in novels and short stories and feel confident about giving feedback on them. I've also had a film script produced and have acted, so feel able to offer some feedback on scripts - though not with as much confidence as with prose. I don't read or write poetry, so I don't claim any special knowledge or insight there. But there's a lot of crossover within the different types of writing so just because someone is, say, a playwright, it doesn't mean that they won't be able to give feedback on prose.
An editor or agent might not be able to write themselves, but they know what makes a good piece of writing. Or certainly a sellable one! They should also know about the business of publishing, probably far more than the average author does. A good editor is worth their weight in gold and is probably more able to give feedback on a wide range of writing styles than a writer might be able to.
Teaching is a skill that not everyone possesses. A good teacher makes difficult concepts easy, classes fun while being informative and so on.
Watch out for...
Experience and/or qualifications as an English teacher doesn't automatically make someone able to teach creative writing, especially if they're used to teaching at school level and you're an adult.
Be aware that just being regularly employed is not a mark of a good teacher. Sometimes they are judged by qualities other than teaching ability - I have heard of a writer who gets a lot of work at a particular university, despite getting complaints about his teaching style, because his students routinely get high marks which makes the university look good. Who does the marking? Why, he does, thus guaranteeing more employment. Word of mouth is very important to guard against this.
The publication record that doesn't really exist. Self publishing doesn't count, unless that's what you're aiming for.
The cynical writer - type 1. They're out there, and can be bitter about publishing. I've heard of a creative writing tutor telling their students that there was no point in even trying to get published, it was so difficult to get in.
The cynical writer - type 2. They believe that teaching is a doddle, money for old rope. I've actually heard a writer say that people were so grateful to meet a published writer, that's all you needed to do.
But don't let the fact that there are some not so good creative writing tutors out there stop you from joining a class. You can learn something from almost anyone, and making a commitment to going a regular class will help motivate your writing. Overall I think writing classes are great, no matter who is teaching!