Fun problem! Here is my take. The bulk of the work is done via a regex, and since the target delimiters appear first, reversing the string makes the matching easier. I do not recommend this solution for production, but rather as a learning experience. It assumes the roles are uppercase characters between 2 and 4 chars in length.

use strict;
use warnings;

my $str = scalar reverse "QB Carson Palmer RB Chris Ivory RB Eddie Lac
+y WR A.J. Green WR John Brown WR Davante Adams TE Martellus Bennett F
+LEX Jeremy Hill DST Panthers";
for ($str =~ /(.*?[A-Z][A-Z][A-Z]?[A-Z]?)/g) {
    $_ = scalar reverse $_;
    chomp( my ($role,@name) = split );
    print "$role -> @name\n";
}

__DATA__
DST -> Panthers
FLEX -> Jeremy Hill
TE -> Martellus Bennett
WR -> Davante Adams
WR -> John Brown
WR -> A.J. Green
RB -> Eddie Lacy
RB -> Chris Ivory
QB -> Carson Palmer
[download]

L-LL-L--L-LL-L--L-LL-L--
-R--R-RR-R--R-RR-R--R-RR
B--B--B--B--B--B--B--B--
H---H---H---H---H---H---
(the triplet paradiddle with high-hat)