It does make sense. Flask is a bottle.
We live from a perfume of an empty bottle. I'm thinking about the meaning of it. To live because of a perfume that's in the bottle, but there's none in it... Maybe it means something sad, that the person isn't "living"...
For me it could mean that someone feels that his/hers relationship of love is not good, but it wasn´t always like that. He/She has good memories but it is in the past, there is nothing in the present.
Not "live of"; that is nonsense. "live off" or "live by" would be okay.
There is a similar expression in English: "driving on fumes" meaning your car's gas tank is so empty that only fumes (odor) remain and you are trying to use every last molecule. Maybe because you cannot afford to buy more.
Now that it was edited according to a native English speaker's comments,("live by" instead of "live of" I think you can validate the translation, samanthalee...