Fuente: http://foro.comunidadjoomla.org/viewtopic.php?f=21&t=793
Fuente: http://docs.joomla.org/Creating_a_file_uploader_in_your_component

Por defecto en la configuración global de no se activa la subida de imágenes mediante Flash (no confundir con la inserción de flash en Joomla).

El motivo, suele ser por conflictos que se dan con un parámetro de la Configuración global. Para descartar esto, prueba lo siguiente:
Administración >> Sitio >> Configuración global >> Pestaña “Sistema”

Busca “Habilitar subidas en flash” y selecciona “No” (Instalación por defecto).

Guarda los cambios.

Explicación:

En realidad no es un problema de Joomla! , si no un bug generado en el fancyuploader (librería de terceros) por la actualización de seguridad del Flash Player 10. El problema afecta a todas las versiones menores o iguales a Joomla! 1.5.7. Este error ya fue solucionado por el desarrollador de fancyuploader (http://digitarald.de/journal/54706744/fancyupload-for-flash-10/), pero dicha librería todavía no fue actualizada en Joomla! (Ultima versión lanzada). Por lo cual, la opción de subir por flash aparece por defecto desactivada.

Flash COOKIE bug on non-IE browsers

Also you should pay attention to Flash player cookie bug!

It is described here http://swfupload.org/forum/generaldiscussion/383

The Flash Player Plugin for , Opera and Safari (and probably other non-IE based browsers) has a bug which sends persistent cookies from IE to the upload URL instead of the cookies from the browser. Session only cookies from IE are not sent.

1) Any cookies from a non-IE browser (ie, authentication, login, etc) will not be sent with the file upload. Rather the cookies from IE will be sent. So, no cookies or the wrong cookies will be sent. In most cases this means sessions and cookie based authentication are lost when making an upload.

2) Cookies set by the upload script do get set, but only for Flash. The browser will not see them.

3) This bug affects Flash 8 and Flash 9 and all versions of SWFUpload

4) You cannot rely on cookies when using SWFUpload (or any Flash based upload tool). You must send the data you need from the cookies in another way. There are several threads regarding this issue in the forum and many of the demos show workarounds for restoring PHP sessions and some sample files show how to restore the cookies so Session and Authentication are restored in ASP.Net.

5) This could be considered a security issue but probably not severe enough to actually compromise any data. The cookies created in IE by Flash still have all the rules and restricts associated with cookies in any browser.

Solution is modify function _start() (libraries\joomla\session\session.php):

$sn = session_name();

if(isset($_COOKIE[$sn]) && isset($_POST[$sn]))
{
$_COOKIE[$sn] = $_POST[$sn];
session_id($_POST[$sn]);
}

session_start();