Will Yaz or another anti-androgenic BCP help with genetic/FPHL?

This is a good question and you’ll want to sit down with your dermatologist to review the many aspects of your question and its answer. There’s lots to think about here. Certainly, oral contraceptives lower adrenal and ovarian androgens and supply estrogen which can help some women with androgenetic alopecia. In other words this can be a type of treatment although often not sufficient. Anytime one starts or stops birth control it’s possible to get shedding and anytime an individual with androgenetic alopecia gets shedding they can worsen their overall hair loss. Be sure to speak to your physician about these issues. There are many reasons that some women choose to stay off the pill - these too need to be discussed. 

Testosterone is generally not a cause of hair loss in women, but it may be in special types of medical conditions such as PCOS (polycystic ovary syndrome). Drospirenone/Estradiol can cause hair loss (see Drugs.com). In fact, many drugs (if you read the label carefully) state in their side effect profiles that hair loss is a possibility. I’ve seen that Yaz’s list of rare side effects does say “increased hair growth, or loss of scalp hair” — so I guess it means that you could see more hair growth (not specifically on the scalp) or lose your head hair. You should not be choosing medications (birth control) based on improving your hair condition.
There are few drugs that are associated with hair growth, but unfortunately none of them will help your cause. For example, minoxidil (the active ingredient in Rogaine) can cause hair growth all over your body when taken orally, not just on your scalp — but please, do not drink minoxidil. I was referring more to the minoxidil oral pill called Loniten, a blood pressure medication. Also, finasteride (Propecia/Proscar) when taken orally, can help with genetic male pattern hair loss (not female hair loss).