You could possibly do it with Peoples, but a custom snippet would be a lot more efficient.
Something like this (assumes that you don't need the username):
$profile = $modx->getObject('modUserProfile', array('phone' => $phone));
if ($profile) {
$placeholders = $profile->toArray();
$modx->setPlaceholders($placeholders);
} else {
return "User Not Found";
}
You'd have to make a form and have the snippet get the phone number when it's submitted. The problem is that the phone number would have to be formatted exactly as it is in the database, and that may vary from user to user unless you format it when you first save the user.
You could solve that by creating a drop-down list of phone numbers to select from, but your users probably wouldn't approve of having their phone numbers available to bots.