This is a complex sentence. It presents ideas out of order, it uses metaphor for dramatic effect, and some details are unspoken.
Simple English translation:
This photograph is from the year 1900. The person in this photograph was employed as an attendant. The attendant's employment involved bathing-machines on the coast of England. Around the time of this photograph, public opinion was changing about what was moral and proper. Public opinion was against impropriety at this time.
The Bathing-Machine was a device for allowing women to swim or bathe in the sea without being seen. In England in 1900, a woman was expected to be fully covered below the neck at all times, so there was no practical way to swim without inviting scandal. The Bathing-Machine was a small room on wheels, where a woman could change into a bathing suit and be rolled to the sea. From there, she could enjoy the water, wading and splashing as she likes, and satisfy the demands of modesty.
The bathing-machine attendant was responsible for moving the machine into and back out of the sea, as well as guarding the women's valuables. This is a job that only exists if society demands that women use Bathing-Machines to preserve their modesty. As bathing suits became more acceptable, the need for Bathing-Machine attendants disappeared.
The author has decided to make this story more colorful and dramatic by adding metaphors. Here are a few of the phrases explained:
"In an age" : An "age" can be any time period with a specific quality that sets it apart from what came before and after. The author is talking about the time period during which morality was just beginning to shift.
"beginning to flirt with impropriety" : To flirt with someone is to engage in light, romantic banter; To flirt with something is to approach it with the same kind of cautious engagement. This phrasing has a double-meaning, since it describes the very cautious early stages of a change in morality, using a word that implies sexual mischief.
"a new morality threatened" : From context, we know that when bathing suits become acceptable, the Bathing-Machine is unnecessary. Therefore, the Bathing-Machine Attendant could become unemployed as a result of a change in acceptable behavior. In this sense, the Bathing-Machine Attendant's job is threatened, not by violence, but by change.