This is very strange—we were assuming that _JAVA_OPTIONS will be picked up by all JVM processes. The only explanation of this to me would be that DynamoDB process doesn’t use Oracle JVM but instead uses OpenJDK (which might or might not have support for _JAVA_OPTIONS built in), but I don’t think that’s the case.
Anyway, it would be necessary to find a way to pass the -Xms256m -Xmx512m flags to the DynamoDB process. How are you launching it right now?