Steve:
I wouldn't put down sheet vinyl flooring. It's slippery when wet and, depending on the kind of backing, it can be soft and may tear if you need to move the washer or dryer over it for repairs. There are thousands of accounts on the Internet of people tearing their kitchen sheet vinyl flooring as a result of moving their fridge over it. Flooring manufacturers recommend sliding plywood under the fridge first and then sliding the fridge over the plywood, but you might not have room to do that in a laundry room.
If you're intent on vinyl, then go with a true linoleum like Marmoleum or Congoleum, which are very much stronger and less prone to tearing than a relatively soft sheet vinyl. Also, an inherent problem with sheet vinyl is that if water ever gets under that sheet vinyl, and mildew starts to grow in that wet area, it will discolour a purplish brown the same way you often see around toilet bowls in bathrooms with sheet vinyl flooring.
I wouldn't opt for a painted floor either because it can be dangerously slippery when wet.
If it were my house, I would go with a synthetic rubber flooring here. That will give you a look somewhat similar to sheet vinyl, but in a very much stronger and more durable material. Johnsonite is the biggest name in synthetic rubber flooring, and they make textured synthetic rubber tiles in a wide variety of colours and quite a few different textures. The rubber is 1/8 inch thick and comes in 2 foot square tiles which are glued down to the concrete. And, of course, rubber will stand up to the pounding of an out of balance washing machine dancing all over the floor much better than a sheet vinyl will. Synthetic rubber flooring is very durable, but it's also quite expensive. However, laundry rooms tend to be small in area, so the cost difference of opting for synthetic rubber shouldn't be significant. Finally, synthetic rubber is inherently slip resistant even when wet. And, rubber on rubber has a very high co-efficient of friction, so walking on textured synthetic rubber flooring with sneakers on is safe, even if the floor is wet.
'Roundel Solid Color Rubber Tile'
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Johnsonite synthetic rubber floor tiles can be ordered in any of these hundred or so colours:
'Johnsonite > Flooring Products > Rubber Flooring > Roundel Solid Color Rubber Tile Product Details'
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And, each colour can be ordered in any of these two dozen or so textures:
'Johnsonite Rubber Flooring'
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And, of course, you can order the tiles in two or three different colours to create patterns on your floor if you want.
Johnsonite synthetic rubber flooring is also available in sheet flooring, but I'm not sure of the dimensions. Normally, roll flooring like sheet vinyl and carpet comes in 12 foot widths with 6 foot width often available as well, but I don't know if that also holds true for sheet rubber flooring.
For more info, go to Johnsonite's web site at
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Generally, the sales people at any retail carpet store won't know much about synthetic rubber flooring because it's normally only used in commercial settings, but if you ask to speak to the store's Commercial Sales Manager, he should be able to help you more and show you both colour and texture sampls.