Export a keyframed animation made in Blender to Three.js (no bones involved) I'd like to export a simple model with a boneless animation. 

I want to know in which format to export because I'm unable to export this kind of animation in .json.

I'd also appreciate some guidance about the code needed to use such animations in Three.js
See threejs docs: https://threejs.org/docs/#manual/en/introduction/Loading-3D-models. I'd recommend trying the Blender glTF exporter suggested there, glTF-Blender-Exporter. It does support keyframed animation.

Once you've exported something, usage is:

var loader = new THREE.GLTFLoader();
loader.load('my-model.glb', function (gltf) {
  var model = gltf.scene;
  var mixer = new THREE.AnimationMixer(model);
  var clip1 = gltf.animations[0];
  var action1 = mixer.clipAction(clip1);
  action1.play();
});

// ... in render loop
var dt = clock.getDelta()
mixer.update(dt);


You can also test your model in three.js without writing code, with http://gltf-viewer.donmccurdy.com/.