When a flaky person tells you they’ll do something, don’t say thank you.
For a flaky person, them saying they’ll do it and you saying thank you closes the loop.
Job done. Little dopamine hit, moving on.
If they say they’ll do something, answer in a way that implies you’ll believe it when you see it.
Something like “OK. I look forward to that,” or, “that would be good.” Leave it open-ended. Loose end.
If they do it, then and only then, say thanks.