You basically have to click once and only once, if you click again you interrupt your attack and need to start over. You do click again to start the 2nd hit of the chain, but only when your sword glows with fire or whatever. The enemy sometimes has a chance of blocking even if you are using the correct stance, so if your attack gets deflected once or twice don't worry. If your attack never goes through, then you're in the wrong stance (z,x,c - pick a different one till you can connect).
If enemies are taking forever to kill, you should give the strong stance (z) additional chances to connect, even if it misses a lot, it does like 4x the damage of the other stances, so when it does go through it will be worth it.
Generally though, you need to figure out which stance to use for which enemy and once you do you always hit.
I really only used igni and ardi or whatever (fire and stun), but neither has cool downs provided you have enough stamina. You have to be close for the fire spell or stun spell to work (like sword distance), until you get the perks to shoot the spells.