The official documentation of Burp doesn't say anything about not working with JVMs apart from the official Oracle Java. There was a time when if we tried to run Burp Suite with OpenJDK, it would start off by giving a warning. But now, it runs perfectly without any warnings in Kali with OpenJDK.
Kali is a Linux-based distribution that has been specifically created for penetration testing and security testing of applications and networks. Previously, it was known as Backtrack. In the following screenshot, we can see that it runs the OpenJDK JRE and is able to run Burp Suite without any issues:
