How does narcissism play into Jaime never speaking of the wildfire? (Related: I understand why he did that for the sake of the story, but I don’t from a Watsonian perspective. Dude, that will clear your name! You think Tywin can’t manipulate singers and rumor?)

Because Jaime, quite a bit like Tyrion, has this anti-hero identity going on. The ignorant masses despise me because of the best thing I ever did, I’m so misunderstood, I’m also a bad boy because I sleep with my sister, but also I’m better than all of you and I don’t owe anyone an explanation, who are you to judge me, etc. etc. 

As we see here:

“Do you think the noble Lord of Winterfell wanted to hear my feeble explanations? Such an honorable man. He only had to look at me to judge me guilty.” Jaime lurched to his feet, the water running cold down his chest. “By what right does the wolf judge the lion? By what right?”