I was looking around for some emoji's to use on this blog and I discovered a page in Wikipedia containing a massive trove of SVG emoji icons. Available for free under the Creative Comes Attribution 4.0 International license.
You can view all the icons here https://commons.wikimedia.org/wiki/Emoji.
While the emoji's are sourced from unicode.org, the images available there do not appear to be SVG images, rather direct Unicode and Base64 encoded PNG files. The linked icons on Wikipedia's website however are SVGs.
The images displayed in the table on the page are PNG, but if you click them it takes you to a SVG file.