Relying on scraping the Oracle download website causes issues like JENKINS-10556 and JENKINS-10511. It would be better if the JDK installation files were hosted on a jenkins-site and that jenkins installations use this site, and an infrastructure job on jenkins-on-jenkins to update this jenkins-site.

I don't know if the JDK's license allows this, though there is the Operating System's Distributor License for Java, which specifically allows this for linux distros such as Ubuntu to redistribute the JDK. Its FAQ explicitely states that mirror sites are also covered, but that may apply only to mirror sites of Operating Systems (i.e. sites mirroring the Ubuntu distro):

Are my mirror sites covered - can I redistribute the JDK as a downloadable package on the web?
Yes.