Elvis & Otis Blackwell didn't have a falling out, they never met. Otis just stopped writing songs for Elvis because he wasn't interested in writing situational songs for movie scenes and thought he could do more creatively fulfilling work elsewhere.
Quincy Jones & Elvis never worked together or socialized in any meaningful way, his recent comments were just as unfounded as his statements that the Beatles were the worst musicians in the world (they weren't), that Michael Jackson was greedy and stole songs (he was a savvy businessman that used completely legal means to purchase ownership of music publishing), or that Taylor Swift can't write songs (she can).
Elvis was only credited as co-songwriter on:
-The four songs from his first movie, Love Me Tender, which were written by musical director Ken Darby and credited to his wife, Vera Matson. Neither Elvis nor Darby had a choice in this matter, it was handled by music publishing & movie executives as part of the business deal.
-Three songs with Otis Blackwell, Don't Be Cruel, All Shook Up & Paralyzed, the first songs he ever recorded written by Blackwell. Again, this was a business arrangement, and to be entirely fair to Blackwell, this was an incredibly prescient example of the systemic racism in the music industry at the time, something which we have to fairly note that Elvis did earn money from and must acknowledge. To Elvis' credit, after these two, he deliberately never again took co-writing credit on another Otis Blackwell song (and Blackwell wrote for Elvis well into the mid-1960s) or any song he did not at least directly contribute something to.
-Two songs he did at least directly contribute to; he gave his friend Red West the title idea for "That's Someone You Never Forget" and did actually sit down and write "You'll Be Gone" with Red and their other friend, Charlie Hodge.
And obviously Elvis didn't hear rap music in the state we think of it today (basically anything after the mainstream breakout Rapper's Delight), but he absolutely heard and LOVED some of rap's precedents in early black gospel music: https://www.youtube.com/watch?v=Wx0oU1OnHf8
And in fact a later iteration of The Jubalaires appeared as the Jubilee Four in Viva Las Vegas and lead singer George McFadden was the ONLY solo artist Elvis ever sang backup, as Elvis sang on the pre-recorded track they are lip-syncing to: https://www.youtube.com/watch?v=auxik3GdJ_I
And he clearly drew influence from that side of his musical heritage when cutting "Run On" in 1967: https://www.youtube.com/watch?v=mmlgc6znnNA
I don't know where so-called Elvis fans are getting this idea that Elvis would have inherently hated rap music. (Actually I do know, but it's not kind to say in polite company.) He was extremely well documented to be a voracious consumer of music, with a huge record collection spanning a dizzying array of genres, and there's a very good case to be made that he would have at least been open-minded about giving it a listen if not collaborating with rappers.