If you want to go with a vintage vibe I think a mint green would be very fresh with the red floor. Otherwise a midtone grey could be very clean and complimentary.

I would go with a light gray. It's very clean-looking and it would modernize the space a little :) Good luck!

I have to agree with fairviewbonnie...unless you want something equally as bright as the yellow. Then you could go with a teal.

I like benjamin Moore elemental for this room. It would coordinate with the floor and neutralize add sim art with touches of red

Color pallet

Love the red floor very daring. I guess I would paint kitchen walls pale gray as well as 3 of the walls in the dining area. Leave the large wall yellow, maybe tone it down a little or pick another primary color for a bold wallpaper. Large geometric black and white design or white and blue. Here are a couple of photos with wallpaper like what I had in mind.

White is going to be your "best bet" here. Until you choose to loose the red floor, you can look to white on the walls and wall art that pulls the red theme through the space. I love the idea of roman blinds with red accents. Ikea has some amazing B/W prints with splashes of red (scene of Amsterdam with red bicycle). The floor is bold. The wall art can be bold to give some balance. Do do that, you may want to stay "white" on the walls so that the floor and wall art set the stage.

for a vintage look...

a. paint walls white and use robin's egg blue as your accent color:
http://2.bp.blogspot.com/-EtBmCMWpo5o/TpQf-f3vtOI/AAAAAAAAKu0/8p0RM5pSGDA/s1600/housetour-6.jpg

b. paint walls a super pale blue:
http://api.ning.com/files/pC48a-wYcH26OR3HjEg-mAyKJ0g6dz2wp5IDPSJWhsS10NYojGJ*Qag9Pm4Ad7SOsqMpL6qgFJJmWC232ren1yfGKi0mk91s/081811RedFloor.jpg

for a classic look...
paint the walls white and use a black and white printed fabric as your accent.

I was looking at modern kitchens with the color RED as its main accent color. White walls would complement your red and give the kitchen a really sharp look.

I once painted an outside laundry room a green called olive branch and the floor very dark red.

It would look great in an apple green. You get to keep the brightness of the yellow but it is toned down a bit.