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.

And why was her ex involved at all?

I also need an explanation :(