Video Example
Final Comp
Intro
With the nerfs to other comps, as well as the changes to Fiora and Sona this patch, Quinn reroll has reemerged as one of the strongest reroll comps in the game. Like any level 7 reroll comp, the main gameplan is to get to level 7 with econ and HP and then slow roll until you are close to Quinn 3. You can also roll aggressively at level 6 to stabilize the board since the odds for 3 costs at 7 vs 6 are almost the same.
Early Game Board
Ideally you play this comp from Quinn or Reksai drop from orbs. If you don't have that, it's a bit awkward since there's no Demacia unit that holds Quinn items. You could play something like a Samira 2 or Jhin 2 to hold the items, but then you need to play an opener that's completely different (Challenger/Noxus or Ionia). That being said, you could always play 3 Demacia opener and then use one of those units even without traits to hold your items until you can find a Quinn.
Mid Game Board
This is what you should be looking for on level 6 (Kassadin is flex, can be any Bastion or a random upgraded unit). Ideally you hit Quinn 2 Sona 2 Galio 2 to stabilize, but if you aren't win streaking, you can also sac until stage 3-5 or 4-1 and then do a rolldown at level 7.
Other Tips
Legend: Urf can let you get to Slayer or Demacia emblem, both of which are strong in this comp. Outside of that, Poro is likely strongest to take good combat augments. You don't need something like Ornn or Ezreal since this comp doesn't need a ton of items due to Demacia