The term "Tattoo Flash" (the nickname given to tattoo design sheets) started in the late 1800's carnival and circus sideshows where many of the early tattooers would ply their trade. Flash was the term used to describe how the carnival callers would get the crowd to migrate towards their attraction, whether it be a game, food, or a sideshow attraction. You needed "flash" to get the crowds attention. The tattooers adopted the term and would hang their flash in the booth to catch the attention of passers by. The design sheets were hung proudly for potential clients to choose their next body adornment. A lot of the early carnival tattooers would string their sheets of flash together vertically to display them, allowing them to be quickly folded up accordion style for traveling to the next town.
The flash of early European and American tattooers varied quite a bit. The works of George Burchett or Joseph Hartley in England had finer lines and more intricate designs than than the American tattooers like Cap Coleman or Sailor Jerry Collins' simpler bolder designs. They all shared the same common themes in the designs, most of them being military based to cater to the sailors and soldiers who were a good majority of the tattooers clientele. Ships, anchors, eagles, mermaids and hearts of lover were engraved in the flesh of soldiers around the globe as a right of passage.
It was very common for tattooers to share the designs with other tattooers they corresponded with, so you'll variations of the same designs from different artists. In the early days tattooers had 30 to 40 sheets of flash hanging in the shop, and you either chose something from those sheets or you didn't get tattooed. Today flash is used more to inspire ideas in clients as most of the tattooing being done in the world these days is custom designed for each individual client.