How to get Flash on school owned ARM Lenovo Chromebook?

Contact the network administrator.

Adobe Flash? If you can't download it from the Adobe website, you probably don't have admin rights. Most school districts use programs that require Flash so the IT department will usually gladly do it for you. I'm sure there are ways around that but many Districts also are equipped to monitor mobile devices. Changing OS programs may be a violation of the school's acceptable use policy. If they can track the change to you, you'll lose your technology privilege.

I'm pretty sure you can't use flash outside of the chrome browser.