LOL, a question that's right up my alley outside of reefing (take a guess with my screen name!). Fluconazoles is an antifungal. It's mechanism of action inhibits 14-alpha demethylase, an enzyme key in production of the cell wall in fungi. Basically, it causes the cell to leak. It does not have any affect on bacteria. So you're clear. But I would not use it at this point. I know you've got a not so good issue, but as stated by
@Townes_Van_Camp a solid CUC will take care of the issue. And it's something you'll need anyway. Now, that being said, ammonia is not good for a CUC. You indicated that ammonia is on the way out so there shouldn't be an issue. Just stop dosing ammonia if you haven't already.
A HUGE part of this hobby is patience. There is always the temptation to bring out the big guns and nuke the issue. And it's not always appropriate. With the lights off and a CUC in place, you're inhibiting the algae's ability to propagate AND getting rid of it by turning it into food for naturally occurring lifeforms. Your tank will be OK. Just go with the flow and keep on keepin' on.