What is the best method of removing vinyl flooring down to the concrete slab?

The first question is how old is the vinyl? Floors installed mid 1980 or before may have asbestos in the adhesive. Floors 1970 may have asbestos in the tile. So, for your health sake, think about this issue and if you feel a need, hire an abatement company. Mesothemolomia is nasty and isn't cureable.
That said, and if you feel the project is safe, there is an acid - muric ? - that will lift the adhesive off the concrete and prepare it for a new floor finish. Check your home improvement store.
Good luck.

Although asbestos was banned in 1977 the feds allowed stockpiles of adhesive to be used up (what were they thinking) well into 1980 , so just how old is that floor? If it is newer than 1980 you can try Krud Kutter Floor Adhesive Remover, Supreme Chemicals of Georgia, Inc. do not use muriatic acid, the fumes will harm you and not budge the adhesive.

Would a simple sanding and power wash work?

No and no . Neither approach will work with adhesive.