Twin flames have a Divine spiritual connection. They are embodiments of each other because they share identical souls. This is where it starts.
Aside from the personal testimonies of each twin flame, there is no scientific evidence, beyond presenting side-by-side facts from two people who lived parallel lives. What happens to one twin flame, happens to the other twin also to some extent. The details for each may be different, but if one twin cries, the other will too. If one twin schedules a vacation to a certain country, the other twin will too. But, in short, you have your own free will, that's why you go through certain paths that bring you closer to your twin or away from you. And at a divine time, the twins supposedly meet by coincidence, as their souls work on this in the background. Why two twin flames meet, even, for once in life, maybe science has no word on this subject but souls and of course your guides know the answers well. And, at the end of the day, you can say it's not scientific proof. However, when you line up all the events side by side and the parallels between you and your lives are more than the differences, how much evidence do you need in order to admit that you just have to listen to your intuition as you move forward on the journey of twin flame.