To generate a RFC 822 compliant date from a MySQL one, you can use the following code sample :
$rfc_822_date = date ('r', $mysql_date);
It formats the date to a RFC 822 one. Make sure your MySQL date is a UNIX timestamp and not the default YYYY-MM-DD date.
Last but not least to properly generate the RSS feed, you have to make sure it's XML, not HTML :
header ('content-type: text/xml');
And voilà 🙂.