How to add new column to existing table in Magento programmatically?

sales_flat_order is the full name of the table and so you have to use alias in $installer->getTable()

In $installer->getTable() parameter like module_alias/table_alias.

In that case try with

$installer->getTable('sales/order')

When you write this it will return table name sales_flat_order

because

module_alias = sales

table_alias = order

---

EDIT

You can use below script to add new column. It works fine in my system

$installer = $this;
$installer->startSetup();

$installer->getConnection()
->addColumn($installer->getTable('sales/order'),'custom_value', array(
    'type'      => Varien_Db_Ddl_Table::TYPE_TEXT,
    'nullable'  => false,
    'length'    => 255,
    'after'     => null, // column name to insert new column after
    'comment'   => 'Title'
    ));   
$installer->endSetup();

I am using Varien_Db_Ddl_Table::TYPE_TEXT insted of Varien_Db_Ddl_Table::TYPE_VARCHAR because TYPE_VARCHAR is deprecated

You can check @ Varien_Db_Adapter_Pdo_Mysql::$_ddlColumnTypes

And If you specify type TYPE_TEXT but set length to lets say 255 Magento will create a MySQL column of VARCHAR type.

You are misusing the method addColumn:

public function addColumn($tableName, $columnName, $definition, $schemaName = null)

the fourth parameter is the schemaName, in your call, the fourth parameter is 255.

->addColumn($installer->getTable('sales_flat_order'),'custom_value', Varien_Db_Ddl_Table::TYPE_VARCHAR, 255, array(
    'nullable'  => false,
), 'Title')

If you use the right parameters, it should work.

I realize this is a relatively 'old' question, but as it's still pretty find-able by Google, I decided to add this bit of information.

Regarding your question, if you want to change the sales/order table, this should not be done by the traditional install scripts/setup. The Mage_Catalog module uses a different Resource_Setup class, namely Mage_Sales_Model_Resource_Setup.

If you want to add attributes to the sales/order model, in order to ensure everything is added and processed correctly, add your attribute like this:

<?php

// Start setup
/** @var Mage_Sales_Model_Resource_Setup $installer */
$installer = new Mage_Sales_Model_Resource_Setup('core_setup');
$installer->startSetup();

// Gather info
$entityType = 'order'; // Adding attribute to this entity type (must be written out in text, not the entity type ID!! That'll not work.
$attributeName = 'my_attribute_code'; // Your attribute code/name

// Add attribute, very few parameters are accepted.
$installer->addAttribute($entityType, $attributeName, array(
    'type'              => 'varchar'
));

// End setup
$installer->endSetup();

Should you wonder why, then the answer is within the addAttribute() function of the Mage_Sales_Model_Resource_Setup class:

/**
 * Add entity attribute. Overwrited for flat entities support
 *
 * @param int|string $entityTypeId
 * @param string $code
 * @param array $attr
 * @return Mage_Sales_Model_Resource_Setup
 */
public function addAttribute($entityTypeId, $code, array $attr)
{
    if (isset($this->_flatEntityTables[$entityTypeId]) &&
        $this->_flatTableExist($this->_flatEntityTables[$entityTypeId]))
    {
        $this->_addFlatAttribute($this->_flatEntityTables[$entityTypeId], $code, $attr);
        $this->_addGridAttribute($this->_flatEntityTables[$entityTypeId], $code, $attr, $entityTypeId);
    } else {
        parent::addAttribute($entityTypeId, $code, $attr);
    }
    return $this;
}