As a smoker I suspect that there is a typo in your sentence:
A reliT cigarette never tastes the same, and that's all I'll preach about rekindling an old flame.
Which refers to the fact that when you extinguish a cigarette and light it again afterwards, it doesn't taste the same as when you originally lit it.
The sentence tells you that rekindling an old flame, which means restarting a relationship with someone you broke up with, is like relighting a cigarette. It may seem like a good idea, but you will be disappointed because it never will be the same as it used to be.