Hillary Clinton

The nominee does not speak until they receive the nomination. If Sanders is still contesting it, he's not going to get to speak unless he wins the nomination. The same is true for Hillary Clinton. She is not going to speak while in contention for the nomination. She will speak after she receives it. Neither is going to get to speak at the convention while they are in contention for the nomination and only the nominee will speak after that. What Sanders wants is for them to change the rules and allow him to speak before the nomination is settled, which is unprecedented and frankly, unfair to Hillary, who will not do the same.

Edit: Now to add a little history, Yes, Ted Kennedy did give a speech after losing the nomination. That was a much longer convention however, and his speech was a tepid endorsement of the candidate. Seeing how Sanders takes losing, I doubt anyone will want to take the risk of him doing something rebellious publicly and souring the historic nomination of the first female nominee.