When I used the snap installation of Brave, I could use Yubikey to sign into google, twitter and facebook. After update to version 0.59.35 Chromium: 72.0.3626.81 (Official Build) (64-bit) I get this error message:
Something went wrong. Please re-insert your security key and try again. If that doesn’t work, try restarting your browser. [Try Again]
I’m not sure if this is related, but chromium 72 introduced a WebAuthenticationProxyCryptotoken feature that enforces the websafe-base64-encoding based on the FIDO U2F specification. You could run a test to see if it works when the flag is disabled.
To disable the flag, completely shut down and relaunch chromium from the command line with the following flag set:
–disable-features=WebAuthenticationProxyCryptotoken
Reference for developers:
Hello, sorry about this. The snap isn’t officially supported.
I am not on snap any more, proper install. And the Yubikey doesn’t work. 
Interestingly, Latpass + Yubikey works fine.
What Brave version on which OS are you currently using with which model of Yubikey?
Linux Mint 19.1, Version 0.60.45 Chromium: 72.0.3626.109 (Official Build) (64-bit) , YubiKey NEO
Looks like there might be a new Chromium bug about this, so I’m holding off on this particular report until we get that sorted out.