I would say that a single stage flash flash evaporator is only the same as a "single stage distillation" because it is seperating components by boiling point. Without any rectification the semantics of calling it "distillation" seem unlikely to help out in any calculation or design.
The only real design aspect of the equipment is the pressure control and vapor fraction control. The pressure is usually controlled by vapor outflow (vapor product) or condensing rate (liquid product via variable area control). Feed temperature will determine vapor to feed rate. The feed will have a temperature controlled heater and feed control valve. The bottoms is always just level controller and valve (probably via a LC->FC->valve cascade).
There are only 4 controllers needed. For the simplest case: feed rate controlled by valve on feed. Flash pressure controlled by valve on vapor. Vapor flow rate (or V/F ratio) controlled by valve on steam heater (feed temperature). Level controlled by valve on liquid.
The calculation determine the product composition is two steps. First, a simple flash calculation to find the temperature and product compositions given pressure and vapor fraction (for example). Second, a feed preheat calculation via an energy balance to find the required feed temperature to get the desired vapor fraction.
best wishes,
sshep