I had a clicky nurser, too. DD was excessively clicky, and had a latch like a steel trap. So she'd latch too shallowly and then I'd have to jam my finger in between her gums to try to pry her mouth open so I could get her to let go and relatch properly- I was so horribly blistered the first few weeks, it was really painful. I was very insistent about waiting until her mouth was open very wide before letting her latch, and taking her off right away if she slipped and she figured it out eventually. Both of my sons are apparently clicky sometimes, but not always. I just readjust and it works out.
DD also clicked more when the flow was very fast, and I think a bad latch was her way of controlling my overactive letdown or whatever it was- when I was more engorged she would often choke a bit while trying to nurse, and then she'd latch on to just the nipple if she could and start clicking. Everett does the same thing now too- if he's sleepy and not hungry and is just trying to comfort nurse but stuff keeps coming out (!) then he clicks and tries for a very shallow latch.