The hypothalamus is the gland responsible for apetite, sleep cycles, sex hormones and body temperature. A sudden drop in estrogen directly affects the hypothalumus.
Hot flashes are usually associated with menopause (as the previous answer says) because during this time estrogen, progesterone and testosterone levels drop. Hot flashes, however, certainly can be experienced well before menopause. I know from personal experience.
There could be many factors which could cause hormonal fluctuations in a woman's body - typically anytime after menstruation has started. Hot flashes for a woman who is too young to be going through menopause is an immediate sign of a chemical imbalance. More commonly, during and after pregnancy (especially if the woman is breastfeeding) estrogen levels are very low. Many women experience mild to moderate hotflashes during this time (it's like nature's way of preparing us for the rest of our lives!).
Usually, if a girl begins menstruating at a young age, she will probably go through menopause at an older age. Girls who start their periods later than average (15 yrs +) typically start menopause earlier than average (possibly in the 40s). But doctors and scientists are now noticing that traditional trends in female hormone behavior are dramatically changing. The average age for girls to start their periods is actually getting younger. Some think this is due to the large amount of synthetic hormones we are consuming in our meat and dairy products.
But to answer your question very simply - I would say that the youngest age hot flashes are possible (although unlikely) is anytime after menstruation has started.
I will assume you are asking about the episodic "hot flashes" experienced by some women when going through menopause. This is highly individualized, most women start menstruating between the ages of 13-17. The beginning of menopause has an even greater range. Some females start to go through menopause as early as the late 30's, some in their 40's, and then others in the fifth decade of life.
Hormonal changes during the process of menopause is the etiology of the so called "hot flashes". Note that it is common for females to experience these hot flashes, not all females battle this.
Females of any age may experience the hot flashes if they underwent hysterectomy because of the change in the levels of hormones flooding the body every 28 days.
I think from Late forties to the early fifties.