I'm currently working on a site, and can't export SVG's from Sketch itself with no issue, but I am missing the Base64 code. Can I generate Base64 encoded SVG's from Sketch 3 when I export?
No, unfortunately you can't export base64 encoded files directly from Sketch. I checked Sketch Toolbox and it doesn't look like there's a plugin for that either, not yet anyway ;)
Generating base64 data URIs is still a surprisingly manual process — personally, I typically use this base63 encoder and paste in/upload my data.