Am I allowed to use the Pro License for $69 on all of my sites and all of my client sites?
You can use it on all your sites, yes :)
And yes, you can also use it for your clients' sites as well.
For full license information, check:
http://www.microsystools.com/products/sitemap-generator/help/website-sitemap-generator-license/ (http://www.microsystools.com/products/sitemap-generator/help/website-sitemap-generator-license/)