Rotating a football with a spiral...

assuming you modeled your football with the ends up and down. you would only apply the velocity to x and z. and spin on the y axis.

this should work if you put it in update:

 float spin;
 float spinspeed;
 Vector3 facing;
 Rigidbody rb;

 void Start(){
  rb = GetComponent<Rigidbody>();
 spin = 1f;
 spinspeed=20f; //adjust for spin speed of ball
 }
 
 void Update () {
              facing=Quaternion.LookRotation(rb.velocity).eulerAngles;
             spin += Time.deltaTime * spinspeed;
             if(spin>360f){spin=spin-360f;}


                  transform.eulerAngles = new Vector3 (facing.x, spin, facing.z);

                  // if you modeled the ball left and right use this instead:
                  // transform.eulerAngles = new Vector3 (spin, facing.y, facing.z);

                  // if you modeled the ball forward and back use this instead:
                  // transform.eulerAngles = new Vector3 (facing.x, facing.y, spin);

 
 }
  
 
 

why not just have an animation component on the football that loops itself spiraling

You could also use a WheelCollider Component attached to the football and just add motor torque to it. It seems a little counter-intuitive, but if you're like me, and you don't like working with Quaternions, and you have a Rigidbody on your football, this is a good workaround. It's really quite simple, just add a wheel collider component to an empty GameObject child to the Football with its Mesh Collider or whatever it's using. From there just add motor torque to the wheel.

 using UnityEngine;
 
 public class ThrowFootball : MonoBehaviour {
     [SerializeField]
     WheelCollider spiralCollider;
     [SerializeField]
     MeshRenderer footballMesh;
     [SerializeField]
     float throwTorque = 100f;
 
     // Use this for initialization
     void Start () {
         ThrowBall();
     }
 
     private void ThrowBall()
     {
         spiralCollider.motorTorque = throwTorque;
         gameObject.GetComponent<Rigidbody>().AddForce((transform.up - transform.forward));
     }
 
     // Update is called once per frame
     void Update () {
         Vector3 pos = new Vector3();
         Quaternion quat = new Quaternion();
         spiralCollider.GetWorldPose(out pos, out quat);
         footballMesh.transform.position = pos;
         footballMesh.transform.rotation = quat;
     }
 }