What can be done for 2, four foot cracks on a kitchen ceiling?

Wow, that's scary! Have you had a professional look at it? It could be that the floor on which the washing machine is sitting is not reinforced. If the weight of a fully loaded washer (wet clothes) is cracking the ceiling, it may fall through at some point. OR, water is leaking from the washer or plumbing and damaging the ceiling. Getting it inspected would be a good option.

If it is a drywall seam that is cracking that would indicate that the edge of the panel landed in a bad spot during construction. If you want to keep the ceiling un-textured, I would suggest that you have the ceiling covered in 1/4 inch wall board, making sure that the seams don't line up with the original seams. If your house is open concept this fix probably isn't feasible. In that case perhaps you could take out half of the surrounding boards and install a new sheet that doesn't have a seam in the same spot. In your three repairs did you try using mesh instead of pape tape? I have used mesh over cracked plaster with great success, but dry wall that moves is always problematic. If you would rather come at the problem from upstairs, you could always reinforce the subfloor in your laundry with some 3/4 inch plywood, so that it moves less when the washer is running. OR if none of this is doable for you perhaps some faux beams in the kitchen to hide the crack.

Buy laminate flooring in a light tone and nail it across the ceiling. It will look like ship lap. Don't forget to put up corner round or other molding at the walls.

I'm sorry but that sounds like a structural issue. The only thing I could think of, besides reconstruction, would be to move the washer down a floor.

I agree with Artemis and P632xp. Obviously the floor wasn't made to handle the weight of a full running washer. Either have the floor reinforced or move the washer and dryier to a lower level.

Move the Laundry equipment otherwise the whole ceiling will fall in. It was obviously not built for the purpose............