like in 'just not show them' ?

There are plenty of skins who don't show them,
I suggest, take a look kin those skins.
Its not the ready made sollution, but I'm sure you will learn a lot from it.

Go look in the _main.php file from a skin that does not show flags and look for the difference...

I was hoping to find out the location for the specific piece of code that controls the flags so that I might remove or change it

for the custom skin, it is this piece of code

<?php
$Item->issue_time();
echo ', ', T_('Categories'), ': ';
$Item->categories();
echo ', ';
$Item->wordcount();
echo ' ', T_('words'), ' &nbsp; ';
locale_flag( $Item->locale, 'h10px' );
?>

change that by

<?php
$Item->issue_time();
echo ', ', T_('Categories'), ': ';
$Item->categories();
echo ', ';
$Item->wordcount();
echo ' ', T_('words'), ' &nbsp; ';
?>

and you have the same but without the flag

I found the specified code in the _main.php for the particular blog that I wanted to modify. I removed it as you instructed and it worked exactly as I had hoped. The flags are gone. Thank you very much, you have been extremely helpful.