Fastboot doesn't recognize OnePlus3 although adb does
I had the same problem with a OnePlus One. The problem is that Windows 10 does not let you install the right driver, assuming you are using Windows 10.

I was able to solve it by using a Windows 7 machine instead.

Another solution I found, but haven't tried, is to disable driver verification. 
This should allow you to install the right drivers, even if the verification fails. However, I do not recommend this as it makes your computer vulnerable to bogus drivers.