OK, so while the full API is still in development, here's how you can use the Brandmarks Logo API right now:
Create an IMG tag in your content (HTML):
replacing the DOMAIN_NAME with a domain that you want a logo for. This is especially useful if you have a database of users that you want to visualize their company, or for a portfolio system that needs to show the companies or websites that people are using.
For example, here at Indie Hackers, it could be used to show a logo for each of the Products automatically, based on the website that is set (hint hint: @csallen).
Give it a go and give me some feedback.