I have the results. This is my Team:
http://i.imgur.com/TpeNs97.jpg
And here are the results:
http://i.imgur.com/HdH3c5b.jpg

It looks, that Ino's Chaos buffed Shizune Mystery skill dmg by ~29%, when I used combo, it increased even more. With 3 Debuff (Chaos, Poison, Blind) it was arround 2230dmg, so ~80% buff. I can assume, that every debuff increase her dmg by ~25%. Increased dmg is only for Shizune's Mystery skill (Poison Cloud) damage, not posion, igniton etc. just that Posion Cloud dmg.. This post was last edited by Shisui7 at 2016-8-24 18:05

I was testing Shizune dmg in turn 1, and only turn 1, without any crits. 1st column is just the try number, second column is the dmg from Shizune Mystery Skill (That Poison cloud), third column was her dmg, after Ino's Chaos skill. It looks, that Her passive works on the dmg from her Mystery skill, not the Poison.

On the left you have just Shizune, on the right you have Shizune after Ino:
http://i.imgur.com/u2iLOJ5.jpg