During his appearance, Trump discussed his bruising campaign style.
"Really, I would like to see the Republican Party come together," he said, "and I've been a little bit divisive, in the sense that I've been hitting people pretty hard" -- prompting Kimmel to crack, "A little bit, yeah."
The host pressed Trump for his thoughts on rivals Ted Cruz and Jeb Bush, asking if he thought either was afraid of him.
On Cruz, Trump demurred, saying, "No, I don't think so." But on Bush, Trump responded, "I think he's scared. He's having a hard time ... I defined him -- I gave him this term, 'low-energy.' I said he's a low-energy individual. We do not need in this country low energy."
Kimmel then steered the conversation to the "baby Hitler" debate. "Someone asked Jeb if he would kill baby Hitler, did you hear that?" Kimmel asked. "And he said he would -- do you think he would kill baby Hitler?"
Trump paused before joking, "No, he's too nice."
Asked by the host if he would have killed baby Hitler, Trump answered, "no comment" but added, "That was a vicious baby, let me tell you."
In the final segment of the interview, Kimmel peppered Trump with a handful of sports and pop culture questions.
On Brady, who has been asked repeatedly about his friendship with the real estate mogul, Trump said, "He's a very good friend of mine, he's a great guy -- by the way, this is a great guy and a winner, a champion, he's fantastic."
Asked if he would go see the new "Star Wars" movie "The Force Awakens," Trump said he might but admitted he's not a big fan of the franchise, only having seen "maybe one or two" because of his busy schedule. "But -- but," Trump added, "great stuff."
The highlight of the appearance was when Kimmel brought out a fake children's book, ghostwritten on Trump's behalf in the style of Dr. Seuss.
The book, "Winners Aren't Losers," lampooned -- in rhymes and cartoons -- some of the biggest moments from Trump's presidential bid.
"Winners aren't losers, they're winners -- like me! A loser's a loser, which one will you be?" Kimmel read.
Other lines from the book alluded to specific episodes from the campaign. "This lobster's a loser, throw him in the pot! I like a lobster who doesn't get caught," the book reads, a reference to the controversy Trump provoked when he disparaged Vietnam veteran and Arizona Sen. John McCain for having been a prisoner of war.
Another line -- "Now here are some frogs I do not like at all. We must kick these frogs out, and then build a wall!" -- clearly refers to Trump's polarizing proposal to build a wall along the U.S. border with Mexico to combat illegal immigration.
Trump was good-natured and appeared entertained by the book, reading the final line himself: "There are two kinds of people, which one will you be? A loser like them? Or a winner ... like me?"