Tag will prevent you establishing anything else for some time if that is a problem, plus it’s expensive for your given application and I wouldn’t use it round waterways.
Flax is a grass, (monocotyledon) so Tordon won’t control it well. Tordon is for woody weeds as stated above.
Glyphosate would be cheapest and has no residual effect in terms of establishing something in place of the flaxes afterwards.
Flax has a very waxy leaf so using a surfactant would give the best results depending upon how much you have and your budget.
You could also cut and paint it onto the plant neat or in gel form.
Bookmarks