When I try to request original size photos, I am seeing error: com.aetrion.flickr.FlickrException: 0: OriginalUrl not available because of missing originalsecret. 

Only pro-users can have original-photos!

You have about two options.

Handle this exception in your code, as it tells you that there is really no original-size.
Call PhotosInterface#getSizes() to determine the avaliable sizes.