By the time Burgess becomes relevant again, there will be no confrontation between him and Luffy as the latter will be busy with Teach. I would agree with you if Teach was the one using the Mera Mera and Burgess was just there to obtain it for him, though, but I find that unlikely.
And Sabo's motivation seems to be bigger than Luffy. He wants the Mera Mera to make the Revolutionaries stronger or at least to redeem himself from being unable to save Ace. Luffy just wanted to keep the fruit as a memento.
It's not really about Burgess in the grand scheme of things though. Luffy was angry at the idea of ANY member of the BB's obtaining the mera mera, not just Teach himself. Teach didn't kill Ace himself, but Luffy still blames him as part of Ace's death and dislikes him as a result.
Similarly, Teach may not use the fruit himself, but orchestrating one of his crew members to obtain and bastardise the powers Luffy's beloved brother formerly held is going to have a similar reaction. Luffy will blame Teach and it will escalate their rivalry.
I think this will tie into a Jinbei Vs. Burgess match up at the end of the series. Since Jinbei will be the other SH who was close to Ace, and formerly fought against the very same mera mera powers when Ace had them.