Before for loop initialize $header to empty string.

$header = '';//initialize header
for ( $i = 0; $i < $fields; $i++ )
{
    $header .= mysql_field_name( $export , $i ) . "\t";

    echo $header;//remove this line
}

EDIT

Also initialize $data outside while loop.

$data = '';
while( $row = mysql_fetch_row( $export ) )
{
    $line = '';
    foreach( $row as $value )
    {                                            
        if ( ( !isset( $value ) ) || ( $value == "" ) )
        {
            $value = "\t";
        }
        else
        {
            $value = str_replace( '"' , '""' , $value );
            $value = '"' . $value . '"' . "\t";
        }
        $line .= $value;
    }
    $data .= trim( $line ) . "\n";
}