I was asked this question many times over past few weeks. This is what I was able to find out regarding flash/Adobe flex applications support.

Astra QuickTest:

Astra QuickTest does not support testing Flash applications or controls.

QuickTest Professional 5.6 and 6.x:

QuickTest Professional 5.6 and 6.0 support Flash version 5.

QuickTest Professional 8.0 – 8.2:

QuickTest Professional 8.x does not have support for Flash controls.

QuickTest Professional 9.x:

QTP and Flash
Adobe is using QuickTest Professional 9.0’s Test Extensibility feature to develop support for their Flex toolkit. Support will be for applications developed with Flex Builder 2.0, with Flash 8.

This is from HP support site:

Adobe has released Flex 2.0.1; this release includes the QuickTest Professional Flex add-in. The add-in was developed using QuickTest Professional 9.0’s Test Extensibility feature. The Flex add-in is developed and owned by Adobe. Please contact Adobe to see about availability, support details, and pricing.

Adobe is providing the add-in via an automation package that is shipped with Flex Data Services 2 starting in the 2.0.1 release.

Basic information on the automation package with QuickTest Professional integration is here

http://www.adobe.com/products/flex/dataservices/

Users can download the automation package with QuickTest Professional integration here:

http://www.adobe.com/cfusion/tdrc/index.cfm?product=flex

A specific Adobe license is required and needs to be requested from Adobe. No specific Flex license is required on the QuickTest Professional side.

Note:
Support for the Flex add-in is being provided by Adobe. You need to contact the Adobe support organization for help with problems or questions related to the Flex add-in.

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Check the up-to-date matrix for the currently supported versions of Flash/Adobe Flex by QTP (UFT).