Flow refers to blood flow from menstruation (period). Flow can also refer to rap flow (the way a rapper rhythmically arranges the words in a song). Spitting bars refers to rapping cool and interesting lyrics in a rap song; if one's flow is heavy (the crux of the joke: heavy flow can refer both to "a lot of blood in menstruation" and to "good rhythm in rapping"), it might be expected that they're spitting bars. I hate my daughter, Megatron.

flow as in menstrual flow, the literal volume of blood and mucosal lining from the uterus during a woman's period

flow also as in lyrical flow, the use of rhythm and articulation in a rapper's delivery

bar as in a measure of time in music, typically a four beat bar

spitting referring to the rapid and rhythmic delivery of words to a beat

If your [lyrical] flow is so heavy, why aren't you [rapping]?

I also need an explanation :(

And why was her ex involved at all?

That movie was insane, the Washington Square scene was horrible.