According to the documentation, Gradle supports proxy authentication using the system properties http.proxyUser and http.proxyPassword. These are nonstandard (also see the Java documentation linked from the Gradle docs) and need to be supported explicitly by any application that wishes to support proxy authentication.
Setting these values currently has the same results as not doing so, e.g. 407 Proxy Authentication Required.
Attached is a patch to core that adds support for these two system properties. As I am not familiar with the Gradle code base I am submitting this as an issue instead of a pull request on Github.