A selection of conical flasks in leather cases, saddle flasks can be made from glass (many older ones are heavy crystal), pewter, or can be silver or silver-plated.
They attach to the D rings at the front of the saddle and their broad strap passes under the saddle flap & attaches to the girth straps.
Traditionally women in the hunting field would not carry a separate saddle flask and sandwich case, but a canteen which would hold both. I don't believe this tradition is universal - I have a 1920's Swaine Adeney catalogue that features ladies' flasks. However, it is upheld by some hunts, and some sidesaddle classes.