I got this working by following a similar set of instructions for New Relic from https://dzone.com/articles/including-java-agent
In summary, you need to include the agent with the Spring Boot application (I imported it into my local Maven repository as it isn't registered in Maven Central) and register the Premain-Class as the snippet from my pom.xml shows.
<profile><id>appdynamics</id><dependencies><dependency><groupId>org.springframework.boot</groupId><artifactId>spring-boot-starter-web</artifactId></dependency><dependency><groupId>com.appdynamics</groupId><artifactId>appdynamics-agent</artifactId><version>${appdynamics-version}</version></dependency></dependencies><build><plugins><plugin><groupId>org.springframework.boot</groupId><artifactId>spring-boot-maven-plugin</artifactId></plugin><plugin><groupId>org.apache.maven.plugins</groupId><artifactId>maven-dependency-plugin</artifactId><version>2.10</version><executions><execution><phase>prepare-package</phase><goals><goal>unpack-dependencies</goal></goals><configuration><includeArtifactIds>appdynamics-agent</includeArtifactIds><outputDirectory>${project.build.outputDirectory}</outputDirectory></configuration></execution></executions></plugin><plugin><groupId>org.apache.maven.plugins</groupId><artifactId>maven-jar-plugin</artifactId><version>2.5</version><configuration><archive><manifestEntries><Premain-Class>com.singularity.ee.agent.appagent.AgentEntryPoint</Premain-Class><Can-Redefine-Classes>true</Can-Redefine-Classes><Can-Retransform-Classes>true</Can-Retransform-Classes></manifestEntries></archive></configuration></plugin><plugin><groupId>org.springframework.boot</groupId><artifactId>spring-boot-maven-plugin</artifactId><configuration>
<mainClass>YOUR_SPRING_BOOT_MAIN_CLASS_IN_HERE</mainClass></configuration></plugin></plugins></build></profile>
Once the JAR is built, add the javaagent in the usual way, it'll still pickup the configuration from the agent installation directory.