Helen Mckearin's book, American bottles & flasks and their ancestry, lists a section on saddle bottles which date from the 17th century or before. Persian saddle flasks are specifically mentioned. She has some examples that date to the 17th century, although McKearin noted that the term saddle bottle "derived from a seemingly logical assumption, or report of tradition, that travelers on horseback hung this type of bottle on their saddles."
She goes on to say that, "Whatever its common name, the so-called saddle bottle apparently was a ubiquitous type of bottle (or flask), one that had evolved by the 17th century, probably long before. It was a free-blown bottle with flattened body; a long, usually slender, neck, with plain or collared lip----in fact, a long-necked flask, and in spite of its flattened instead of balloon body, it calls to mind Theophilus's directions for blowing flasks with a long neck." pg. 244
If you search by the phrase persian saddle flask on the web, you will find some pictures of these to compare to your own. Please let me know if you have other questions about your flask.
