What is the quickest way to lose neck fat?

Forget quick ways. It will take time. If the overall BMI goes down eventually your neck will also have less fat.

As @mattbrowne said, you can only lose fat in a general way. You can increase muscle tone in specific areas and this will cause a tighter appearance, but you can’t control where fat is lost, short of liposuction.

I’ve heard chewing gum… I think it’s bullshit but it’s worth a try right?

Only two ways. 1) Losing overall weight & 2) Liposuction.
And chewing gum doesn’t reduce neck fat, but it does build up jaw and temple muscles.

Losing weight and toning up will give a little lift but loose skin will always be loose skin, lipo would just leave you crepey unless you had some nipping done along with it. Also, drinking excessively causes a lot of facial bloating, easily seen around the eyelids, cheeks and jowels.

I think what you’re doing and the suggestions posted here plus maybe lie on your back and try lifting your head up in two sets of eight. I think you need to strengthen your neck muscles a little.

a good friend of mine lost a lot of weight (like she was about 300 and she got down to 180 – did it the traditional way, not the band or anything) and she had hanging skin on stomach and she still had her double chin. she got a tummy tuck to tighten the abdomen and get rid of that skin, and the doctor did surgery on her double chin to tighten it up. the tummy tuck looked like extremely painful recovery, i think the double chin surgery recovery was “cake” in comparison.

Properly aligned, the guillotine can be quite efficient and effective.
Some consider this a bit drastic. Some people disagree.