[Celyn]

From my own experiences combined with reading and being involved in counsellor training groups....

Red flags would be:

Promotes one type of therapy over another (while there are some therapies that are highly recommended it's also important to remember that not all types are going to work for everyone).
Isn't aware of their biases (for example, BPD has a big stigma and sometimes when someone is diagnosed or suspected with that, others will treat them differently, causing a reaction in the person who has BPD only to get told that the reaction is from BPD and doesn't acknowledge their part in the process).
Isn't open minded (it doesn't matter how many qualifications or how much experience a therapist has if they can't be open minded about their clients situations).
Doesn't get back to you/cancels on you (personal experience, a counsellor asked if we could take a break, I said okay, the counsellor made a note in her diary to resume in a few months time and I never heard from her and was too anxious to get in touch as I thought she might've been too busy for me).
Assumes things/puts words in your mouth (one counsellor assumed I was scared of something because I hadn't done it but that wasn't the case at all...she assumed I was scared but didn't ask if that was the case).
You feel pressured to continue with them (whether it's external pressure from the therapist or internal pressure that you can't quite figure out).
You feel, for whatever reason, they just don't quite 'get' you (whether there are misunderstandings or not, it's difficult to work with someone that you feel doesn't actually understand you).

I'm guessing green flags would be the opposite of all that. Importantly, they are there to meet your needs (which they should establish at the start) and help you figure out the way forward. They might not know all the answers (and they should know when to refer you onwards if they feel they can't help you) but they should try to tailor their approach to you. Personally, I'd add into the red flags isn't aware and doesn't understand neurodiversity but that's just me