I'm not sure what no-poo method you're trying but I don't see anything wrong with the shampoo you're using. I thought that the whole point of no-poo was to avoid sulfates, but I don't see any in your shampoo. So I guess that could be classified as sulfate-free.
Though, I think that the herbal essence tousle me softly has silicones which is a no-no, especially since you don't have a sulfate in your shampoo to get rid of build up. So, I recommend to change to a silicone free one and clarify with a different shampoo that actually has a sulfate, or even coco betaine (which can also remove silicones, but much gentler than sulfates) to remove silicones and get a fresh start.
Also, a different no-poo method is the baking soda and vinegar rinse version. Though, you don't have to do the baking soda part, but I heard that vinegar can help remove dandruff. Though I don't have dandruff, I use that method sometimes and it doesn't seem as bad. The baking soda can be drying (but you can just stick to your shampoo) so I adjust and lessen the ratio of baking soda to water. I love the vinegar rinse because it makes my hair shinier and the smell disappears when it dries. I also infuse it with herbs that make it smell better, that I actually want the smell to remain! Weird, I know. But thats just my experience.
Or you can try co-washing, which I've also tried. Lots of people use suave or vo5, because it's cheap and has different scents, but I don't think they have any benefits to dandruff other than an alternative to shampoo. Unless, you can find a co-washing approved conditioner for dandruff, you could try that. Do you have a Trader Joe's nearby? I think their Tea Tree Tingle Conditioner can help with dandruff and cleansing though, so I recommend that. I think they only cost $2-$5, so it's pretty cheap. It has natural ingredients and no silicones, so it's a plus. I think some of it's ingredients can also help with dandruff. Plus, it's tingly.
Hope I helped.