How long does it take to fix the iSight camera?

Only your local Apple Store, or a Certified Apple Reseller/Service Center can assess/inform you of the repair timeframe. Apple is not here — only international volunteers that have nothing to do with Apple sales or service.

I'd suggest to you to demand a phone replacement instead of camera replacement.....that's what my wife and I did, just 3 days ago. That's if your using the Apple iSight camera replacement program for the iPhone 6 Plus.

https://www.apple.com/support/iphone6plus-isightcamera/