When I hear "maxi" I first think of a pad. When I get over that, I think of a jersey knit, beachy, kind of clingy but flowy skirt.
However, I think there are semi decent cotton long skirts that you could wear. I have a tiered eyelet one that I wore when I worked my last job and the required dress was somewhere between business causal and business professional. However, the girl who wore the jersey knit maxi was told not to wear it ever again.
Considering that some people in my business-casual office wear jeans, running shoes, and UK t-shirts to work, I think I look pretty damn professional in this dress with dressy wedges. Also - I would never in a million years wear flip flops of any kind to the office.