#!/usr/bin/perl

use strict;
use warnings;
my $flag=0;
while(<DATA>){
        if (/\{AUTHOR\}/){
                $flag=1;
                next;
        }
        if (/^\{/){
                $flag=0;
                next;
        }
        print $_ if $flag;
}


__DATA__
{TAG}
tag1
{AUTHOR}
By June Fletcher
JOURNAL
{TAG}
tag2
TOM MacCUBBIN
{DATA}
data1
{AUTHOR}
Richard White
{AUTHOR}
MacCUBBIN
{SOUR}
[download]

Tou forgot to unset your flag

No, the flag is being set with the result of the expression: $1 eq "AUTHOR"

Moving the condition to the second line (bad idea, because the expression will be evaluated many times even if $tag does not change for some rows):

my $tag = "";
while (<DATA>) {
    ($tag = $1, next) if /\{(\w+)\}/;
    print $_ if $tag eq "AUTHOR";
}
[download]

Removing the next from the tricky array used to have 2 sentences being affected by the if condition to test for a line with braces:

my $tag = "";
while (<DATA>) {
  $tag = $1 if /\{(\w+)\}/;
  next if /\{/;
  print $_ if $tag eq "AUTHOR";
}
[download]

Too many evaluations of conditional expressions. Inefficient, but I guess you got the idea.

BTW, I was assuming that braces won't appear on text lines...

my $flag = 0;
while (<DATA>) {
  $flag = ($1 eq "AUTHOR") if /^\{(\w+)\}$/;
  print $_ if $flag and not /^\{/;
}
[download]