How can I animate my gun when I'm moving

If you've already got your bob animation in the gun then all you need to do is add another script to the gun that says something like

if(Input.GetKey("w"){
  animation.Play("walk forward");
}

this might be a problem if you want to walk forward and shoot at the same time so add an else clause to only play the bob animation when not shooting.

Alternatively you can adjust the position of the gun using a sin wave adjusting frequency and amplitude based on movement speed.

something like:

transform.localPosition = Vector3(0, bobHeight*Mathf.Sin(bobSpeed), 0);

bob speed needs to be incremented every frame for a smooth motion and you need to centre the gun when you stop.

You can also do side to side motion or twisting much the same way.

The advantage of this method over animation is that it's directly linked to movement speed but on the other hand it's more fiddly to get it to look right.

EDIT

Using your example:

function Update () {
   if (Input.GetButton("Fire1")) {
      animation.Play("AnimationEnfield");
   } else if (Input.GetKey("w") {
      animation.Play("AnimationEnfield2");
   }
}

You can also use animation blends to transition between animations

Sorry, I'll put that as an answer so it's easier to read

var fireclip;

function Update () {

if (Input.GetButton("Fire1")) { animation.Play("AnimationEnfield"); fireclip = true; return;

}

if(Input.GetKey("w") && fireclip == false){ animation.Play("AnimationEnfield2"); } else { return; } }