I have noticed that when I use Pale Moon, Duolingo cannot detect that I have a microphone, and the Microphone settings do not appear on the Settings page.
To test this yourself, I believe you will have to create an account at Duolingo. (It's free.)
PM 27.8.2 (64-bit)
Chromium 65.0.3325.181
Ubuntu 14.04.5
UPDATE: Also tried it with Seamonkey 2.49.2 and got no microphone, and with Brave 0.22.13 and did get the microphone.