Might be considered a duplicate of JENKINS-40936, though the use cases are a little different: this RFE applies even to jobs with no manual approval step, and no need for interior milestones of any kind.

While something like an eager flag would be perfect, I am filing a PR showing a workaround: start your Jenkinsfile with

for (int i = 0; i < (BUILD_NUMBER as int); i++) {milestone()}

This is another option:

@NonCPS
void cancelPreviousRunningBuilds(int maxBuildsToSearch = 20) {
    RunWrapper b = currentBuild
    for (int i=0; i<maxBuildsToSearch; i++) {
        b = b.getPreviousBuild();
        if (b == null) break;
        Run<?,?> rawBuild = b.rawBuild
        if (rawBuild.isBuilding()) {
            rawBuild.doStop()
        }
    }
}

Just call cancelPreviousRunningBuilds() at the very fist line of the pipeline.

jglick This is confusingly worded – could it be rephrased as "abort previous running builds even after they've passed the milestone"?

Not necessarily. The milestone step is simply a tool which could be used to implement this. The use case is to abort all previous running builds. See my first comment.

When pushing new changes to a PR, it would be awesome if the multi branch had an option to automatically kill all previous running builds/queued builds for that branch so that only the latest gets queued/built. This way if a developer commits and pushes and then does the same again immediately afterwards we don't have two builds, especially if the builds take 20+ minutes each, and we don't care about the intermediate result.