UPDATE: (I already know this is Flash bug.) I managed to make SWFUpload work on GAE. If anyone faced the same issue, I had to give up on BlobstoreService and I'm parsing my uploads using com.google.apphosting.utils.servlet.MultipartMimeUtils...
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Due the issue SWFUpload has with empty-bodied responses it can not be used on Google AppEngine as its BlobStore uploadURL does not allow any content in the response. 
Is this something that needs to be fixed in SWFUpload or is it Flash bug?
Regards
J. Záruba