Regenerative healing, flowing whip, dissection blade, healing tips, ninja monkey
It's gonna be a bit lengthy so bear with me.
Knockdown, repulse, high/low floats etc. are statuses. Every chase is triggered by a status and produces another status to trigger the next chase. I'll use the lineup you posted as an example.
Total chases = 8, combo triggers are either knockdown (KD), low float (LF) or high float (HF). According to your position, this is what your combo chains look like (correct me if I'm wrong, though).
A KD triggers Hinata > AF Main > Sasuke > Suigetsu > Hinata > Sasuke = 6 combo
A LF triggers Suigetsu > Hinata >Hinata > AF > Sasuke > Sasuke > Sasuke = 7 combo
A HF triggers Sasuke > Suigetsu > Hinata > Hinata > AF > AF > Sasuke = 7 combo
Suigetsu and Sasuke have one similar chase (low float to repulse), but Suigetsu will always move to chase LF first because he's in position #2 ahead of Sasuke who's in #3. If you switch their positions around, Sasuke will move first. But since they chase and produce the same statuses, nothing changes much.
Let's say AF's standard attack produces a KD. Why does Hinata chase it first instead of AF? Same reason: Hinata's at #1 while AF's at #4. The #1 ninja will be given priority to move first, then #2 and so on. Since they produce different statuses, if you switch them around your combo will turn out pretty different.
That's the basic mechanics of chase and combo chains. Basic combo chains depend a lot on your lineup's positions. In your case, your full combo should be 8 considering that all your chases chain together properly.
There are combo chains that don't depend on positions at all, called circle combos. When triggered, it will give you a full combo regardless of how you position your lineup. Try the lineup I suggested (switch out Suigetsu for Kakashi) and use the white snake summon. You'll see how circle combos work :D
Little tip: Try using dissection blade with neurotoxin :P