There are several JDK options available when installing FlexDeploy. The main requirement is that the version of Java used is version 8. if your Linux distribution includes a build of OpenJDK 8 you can use that version.
Amazon Corretto - Amazon's build of OpenJDK with security updates https://docs.aws.amazon.com/corretto/latest/corretto-8-ug/downloads-list.html
OpenJDK - https://adoptopenjdk.net/releases.html
Oracle JDK - Oracle's build for those who are licensed http://www.oracle.com/technetwork/java/javase/downloads/jdk8-downloads-2133151.html