Are there any fashion designers that advocate women's rights or women issues through their fashion works? How could I find information about this?
There are a few ways you could go about researching this topic. First, there are those who would argue that successful fashion designers for women's wear, by default, actively shape the idea of women's rights and issues in everything they produce. Consider that entire decades have been defined through the scope of politics and fashion. In this way, researching how fashion has reflected current events and issues might produce what something you can use.
One designer you may want to look into is Coco Chanel, who worked her way from poverty to riches through her influence in the fashion industry. The 2009 movie, Coco before Chanel, is a biographical tribute to her. Because of this movie, she has recently been a source of new interest in the design world.
Another avenue to go about researching this topic would be to compile a list of current (and big name) designers and look at the charities, causes, or organizations they actively support.
Finally, you may want to work backwards and start with the issue and see what designers have been involved with support. Here, consider the "Red Dress Foundation" (a fashion movement in support of women's heart health) or the National Breast Cancer Foundation (pink ribbons).