How to add an attribute to product_flat_table

Either one of the following attribute settings is true:

• backend_typ = 'static'
• is_filterable > 0
• used_in_product_listing = 1
• is_used_for_promo_rules= 1
• used_for_sort_by = 1

Or you add it manually by observing this event:
catalog_product_flat_prepare_columns

Attribute is not added - source models

If you attribute is still not added it might be, because \Mage_Eav_Model_Entity_Attribute_Abstract::getFlatColumns is called on the attribute, which checks wether a source model exists.

public function getFlatColumns()
{
    // If source model exists - get definition from it
    if ($this->usesSource() && $this->getBackendType() != self::TYPE_STATIC) {
        return $this->getSource()->getFlatColums();
    }
    // ...
}

As you can see, getFlatColums is called on your source model, which default implementation is:

// \Mage_Eav_Model_Entity_Attribute_Source_Abstract::getFlatColums
public function getFlatColums()
{
    return array();
}

Therefore your attribute is not added.

And implementation like this might help:

public function getFlatColums()
{
    $attributeCode = $this->getAttribute()->getAttributeCode();
    $column        = [
        'unsigned' => false,
        'default'  => null,
        'extra'    => null,
    ];

    if (Mage::helper('core')->useDbCompatibleMode()) {
        $column['type']    = 'varchar';
        $column['is_null'] = true;
    } else {
        $column['type']     = Varien_Db_Ddl_Table::TYPE_VARCHAR;
        $column['nullable'] = true;
        $column['comment']  = 'Seals column';
    }

    return [$attributeCode => $column];
}

*Update*

How to fill the field

After the final win that the column is created on the flat tables, it was NULL after reindexing. Something is missing and this is:

\Mage_Eav_Model_Entity_Attribute_Source_Abstract::getFlatUpdateSelect

This method has to return a Zend_Db_Select due to this:

\Mage_Catalog_Model_Resource_Product_Flat_Indexer::updateAttribute
// ...
$select = $attribute->getFlatUpdateSelect($storeId);
if ($select instanceof Varien_Db_Select) {
    if ($productIds !== null) {
        $select->where('e.entity_id IN(?)', $productIds);
    }
}
// ...

An example implementation which works for me:

public function getFlatUpdateSelect($store)
{
    return Mage::getResourceSingleton('eav/entity_attribute')
        ->getFlatUpdateSelect($this->getAttribute(), $store);
}