Déjà je suis née fille, je vais pas en plus venir parler la première.

You could put two more comas in your sentence to make it more understandable :

Déjà je suis née fille, je ne vais pas, en plus, venir parler la première.

In this case you can see that “en plus” mean “on top of that”.
Thought your original sentence doesn’t make a lot of sense, but that’s not the point.

Here is a rough translation:

I was born a girl. I don’t want to speak first on top of that.

En plus means furthermore here.

Déjà je suis née fille, je vais pas en plus venir parler la première.

might be rewritten to:

Déjà, je suis née fille. Je ne vais pas, en plus, venir parler la première.

which might be translated by:

For a start, I was born a girl. I’m not going to take the floor first on top of that.

The first part is unusual. One would expect Déjà, je suis une fille unless the sentence is from a transgender person.

The second part probably means several people are going to speak on stage or something, and the person “born a girl” doesn’t want to be the first one to take the floor, precisely because of being born a girl. The context should explain why (s)he thinks it is a reason not to.