Is it normal to get a double chin when looking down like this for a skinny person? (photos)

In my opinion, you do not have a significant amount of fat under your chin and I would not recommend any treatment.  It is fairly normal for people to develop a double chin when looking down and bending the neck forward.  

Although not all a double fold when looking down, it is not that uncommon. It often relates to genetics, skin tone and also laxity of the skin. There can also be a small amount of fat under the chin that is not that noticeable when one keeps the head in an upright position. If your surgeon determines that there may be some fat, liposuction may help tighten about skin. It is also true as we get older, our skin gets looser! Even skinny guys looking down get the fold in the tummy region as you get older.

It appears you may have some excess fat in your submental area which could be hereditary. Liposuction or Kybella could help you with this issue