Formal:
* Discompose
* Perturb
* Agitate
* Unsettle
* Disconcert
* Throw into disarray
Informal:
* Rattle
* Frazzle
* Throw off
* Throw for a loop
* Get someone's goat
* Put someone on edge
* Make someone nervous
* Make someone lose their cool
The best synonym for "fluster" will depend on the specific context and the desired level of formality.