When job hunting, "skills" and "experiences" are somewhat synonymous, yet at the same time meaningless. Everyone has "skills" and "experiences" so why belabor the point? Just pick one or the other, and concentrate instead on what kind of skills/experience you have that would make you a valuable employee.
My experience in data management and programming makes me the ideal candidate for this position. I worked for ten years managing, etc.
In a different context using two ands is fine, assuming you want both items in the first part to apply to both items in the second part:
The story tells of the lives and loves of Bartelby and James, winemakers of reknown.
If you want to separate out the items of the first part to only apply to one item of the separate, it's best to use a comma or even a period to break them up.
I have advanced skills and extensive experience in data management, as well as some programming ability.
This is awkward, though. I'm not sure why you want to separate out programming, except to point out you're not as skilled -- in which case, why mention it at all?