If you've Googled the names "Elvis Presley" and "Captain Marvel, Jr." together--and who am I to say how you should spend your time?--you've found links to hundreds of webpages repeating the belief that Presley modeled his appearance on that young superhero. The most thorough discussion I've seen is this four-part series at Dial B for Blog.
However, in all those words about Presley and the Shazam! comics, there's no real evidence of a connection between him and Captain Marvel, Jr. Instead, Dial B writer Robby Reed repeats the conclusions of Elaine Dundy's book, Elvis and Gladys (1985). Among Presley biographies, Dundy's is considered one of the more insightful and less exploitative, though still a long way from Peter Guralnick's Last Train to Memphis.
Dundy refers to Captain Marvel, Jr., a lot in her book. Chapter 1 is named after the character. And she makes statements like these:
- “Elvis was already immersed in the adventures of the Lone Ranger, Hopalong Cassidy, Tarzan, Batman, and Superman when his secret life suddenly took a dramatic new turn. He discovered Freddy Freeman in the comic book series Captain Marvel’s Adventures. There, on page 267, young Freddy made his entrance--and very nearly his exit--fishing off a boat with his grandpa...” [page 3]
- “Freddy/Marvel, Jr.,...has been obviously and sensitively copied from a most appealing adolescent life-model. He looks in fact exactly like Elvis, from adolescence to the end of his life, strove to make himself look.” 
- “But the Captain Marvel series, and in particular, Captain Marvel, Jr., was Elvis’ unquestioned favorite. Adding greatly to the popularity of the series were the characters that derived and that sprang up from the stories. . . . Elvis’ twin-fusion with Freddy/Captain Marvel, Jr., was total and it was from reading his adventures that the young Elvis secretly began to create himself.” 
- “It was Captain Marvel, Jr., who styled Elvis’ glistening hair, side-parted with the forelock falling over his brow, the sideburns, the hair growing down his neck. Much later would come Elvis’ Captain Marvel, Jr., cape and lightning bolt emblems on the TCB (Taking Care of Business) and TLC (Tender Loving Care) jewelry he would give to his special friends.” [69-70]
Dundy quotes Presley's own words, from a 1970s interview: “I was the hero of every comic book I ever read.”  He said something similar in a 1970 acceptance speech, quoted at the official Graceland site: “When I was a child, ladies and gentlemen, I was a dreamer. I read comic books, and I was the hero of the comic book.” But those statements don't single out the hero nicknamed Junior. In fact, they imply that Presley had no special favorite.
Lloyd recalled Presley preserving his comic books with unusual care for the 1940s (well before bags and boards). But Dundy doesn't point to any Captain Marvel magazines surviving in his estate. Yes, there are such comics now on display in some museums devoted to him, but they've been put there since Dundy's book was published.
TOMORROW: So what evidence led Dundy to focus on Captain Marvel, Jr.?