The title refers to the fact that Mrs. Muir becomes ill and the captain provides his medicine. Mrs. Muir then dreams about being at a dance or "ball" with the captain. (it has nothing to do with exercise equipment.)
The red flannel hash that housekeeper Martha makes is a traditional New England recipe made with beets, often served for breakfast or lunch using the left-overs, and traditionally topped with a poached egg, which is optional. An alternative can be had by combining a can of corned beef hash and a can of beets, chopped, fried in a pan, and sometimes topped with ketchup.