The part you're asking about is actually fine. On the other hand, just about everything else looks wrong to me. Let's go over the code.

Always use use strict; use warnings qw( all );!!!

open TEST,"@ARGV[0]";
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should be

open(my $TEST, "<", $ARGV[0])
   or die("Can't open \"$ARGV[0]\": $!\n");
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• Use the safer three-arg open over the two-arg open.
• Always check open for errors as it is particularly prone to failure.
• Don't use global variables for nothing.
• Don't put variables in quotes for nothing.
• @ARGV[0] is an array slice, but you want to lookup a single value in the array.

$flag = "ON"
...
$flag = "OFF"
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my $looking = 1;
...
$looking = 0;
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• Your code didn't even compile.
• Limit the scope of variables to where they are needed.
• Use true and false values (such as 1 and 0) for booleans instead of two true values (such as "ON" and "OFF").
• Use meaningful variable names.

while (<TEST>)
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should be

while (<>)
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<> is short for <ARGV>. ARGV is a specical file handle that reads from the files named in the argument list or STDIN if none.

if (/test/ and $flag eq "ON")
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should be

if ($looking && /test/)
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• It's better to only use the low precedence and, or and not for flow control (... or return ..., ... or die ..., ... or next ..., etc).
• When you want to test for truthness, don't check for a specific value.
• $looking is far cheaper than /test/, so we'll move it first.

print "start";
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print "start\n";
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say "start";
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close TEST;
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use strict;
use warnings qw( all );

my $looking = 1;
while (<>) {
   if ($looking && /test/) {
      print "start\n";
      $looking = 0;
   }
}
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The one problem left is that you read "half" the file for nothing. Let's avoid that!

use strict;
use warnings qw( all );

while (<>) {
   if (/test/) {
      print "start\n";
      last;
   }
}
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