How to Get Rid of Fleshy Moles Under Arm and on Neck?

These appear to be skin tags which can be very common.  We usually treat them with either cryotherapy or with shave excision.  

I would seek evaluation by a dermatologist to evaluate possible methods of removal ranging from liquid nitrogen, to shave excision, to hyfrecation, electrocautery, simple excision, laser ablation, etc. Lesions may need to be evaluated by a pathologist.

Skin tags are essentially fleshy protrusions of normal skin that occur in areas with a large amount of friction such as under the arms or in the groin.  Diabetics are prone to skin tags so it is recommended to see a primary care physician to rule out this disease.  Skin tags can be removed with ease in the office either with liquid nitrogen cryotherapy ("freezing") or anesthetizing the base of each skin tag with a local anesthetic and removing them with surgical scissors.  As always, it is recommended to see a board certified dermatologist for diagnosis and treatment.

Those lesions appear to be acrochordons (or skin tags).  They are very common.  There are several ways to remove them including scissor excision, cryotherapy, and many more.  Your dermatologist should be able to remove these the same day that you see him/her.