Addressing this topic will be quite the medical conundrum because it is very hard to prove any type of causality in these types of investigations. Nevertheless, I will do my best to present and explain as much of the current research available to determine if flying and jet lag can affect your menstrual cycle.
A lot of investigations have attempted to prove if frequent fliers are more prone to have irregular periods compared to the general public without drawing a concrete conclusion.
It was determined in one study that when surveying 43 flight attendants who were employed full-time with an airline industry reported to have changes in their menstrual cycles in 21 percent of cases. These flight attendants were on routes where they would have no more than 1 hour of time zone changes. This same study also found that women had higher levels of thyroid dysfunction, cervical erosion and levels of insomnia compared to healthy women so as you can already imagine, it is hard to say what causes what in this circumstance. Questionnaires are often unreliable because you are unsure if the correspondents are truthful and even if the numbers report accurately, being tired from the demanding nature of the job could subconsciously make women think that their periods are more severe when in reality, there is no observable change. 
In another study, flight attendants on longer flights were assessed to determine if they noticed any changes in their menstrual cycle during international flights. In this investigation, 200 flight attendants were asked about menstrual cycles and about 50 percent of flight attendants reported menstrual cycle changes during their flights. The changes of this cycle was where it was hard to draw definite conclusions. Roughly half of the flight attendants reported that their menstrual cycle flow was higher than normal during the flights while the other half of the population reported that their menstrual cycle stopped entire or that at least the flow was significantly reduced only to have it return to levels that were greater than normal by the time the flight landed once again.
Whether you are a flight attendant or just a frequent flier, something to ease your mind is the fact that although you may have irregular menstrual cycles during your journey, studies show that there will be no impact on your changes for becoming pregnant in the future. Active and retired flight attendants reported infertility rates that were quite similar to the general population.  My best advice for you is to just pack your carry-on bag accordingly to make sure that you are prepared for any situation that may occur while the "wheels are up." You may be uncomfortable during the flight but you will not have any long-term risks to worry about based on current data available.
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