It is possible to use Flex SDK 4.5 in Flash Builder 4.0.1
Upgrading ArcGIS Viewer for Flex 2.3.1 to Flex SDK 4.5 produced the following errors:
1.Required skin state missing errors:
normalWithPrompt, disabledWithPrompt
Solution: Insert this right before the line with the problem:
[States("normalWithPrompt", "disabledWithPrompt")]
Reference: http://forums.adobe.com/message/2574211
2. Minimized widget with large canvas
Solution here:
http://forums.arcgis.com/threads/29750-flex-sdk-4.5-support