If you're cropping, saving and then uploading the updated, cropped, saved file, there is no way Flickr could be adding in the bits you cropped out, it just can't happen. As far as I can see it, that leaves two possible scenarios:
1. You're somehow undoing the cropping before saving
2. The files are getting saved under different file names (something like IMG_123(1) instead of IMG_123) and you're accidentally uploading the unmodified versions