Nothing happens when I attempt to generate account-linking code in Rock Band 3

It is no longer possible to achieve this goal / achievement / trophy, due to changes in the layout and functionality of RockBand.com. Here's what Harmonix has to say about it:

We’re sorry, but account linking is no longer available for Rock Band 3 on RockBand.com. The layout and functionality of RockBand.com has changed considerably in the years since the release of Rock Band 3, and as a result account linking is no longer functional. If you have not linked your account previously, you will not be able to complete the “Well Connected” Career Goal or the “Well Connected” achievement / trophy in Rock Band 3.

Source.