blue is perfect for oak. did you see all the colors I posted in my other comment? I put a few blues in there. this blue would look really nice w/the oak I also like the greens. Sage greens look great w/oak and will work w/your green frame. This is Silver Sage SW Svelte Sage Behr,,Quiet Moments bring home some other samples (if you use Behr, you can get the $2 samples. BM is at $7 each. )' these are some gray/greens and would look nice. I don't like the blue/grays w/the oak because those paints tend to run on the 'cool' side, whereas oak is warmer. Pale Oak (BM) may be nice for the other rooms. maybe try this link for the best wall colors w/oak cabinets https://www.hometalk.com/2389914/5-top-wall-colors-for-kitchens-with-oak-cabinets this one is Pleasant Valley

You definitely need some color, personally whites, creams and anything in the brown family is drab. Try a matte mossy green, or light olive tone. The lighter greens go well with your trim, add color, and a welcoming feel.

First things first: make sure you can PURCHASE more of the Pergo. And then, just for fun, make sure this is the Pergo that is water RESISTANT. If it is NOT, then do not run this in the kitchen. And if you have it in a FULL bath (shower/tub) then I recommend you look at a different floor - in the next 5 years. So, now that you have established it IS the water resistant Pergo AND you can STILL PURCHASE the product, you can decide if the colour clash with your cabinets will be worth it. Traditionally grey toned wood (like the Pergo) does NOT look very happy with orange toned wood (like oak cabinets finished in an oil based finish commonly referred to as "honey oak"). This clash can be reduced by working with a DARK GRAY counter top (a counter that is SPECIFICALLY chosen to match the Pergo). So....that brings us the the next question: what is your counter top? And then we move to "When do you want to renovate the kitchen?" If you have a kitchen renovation in your future (next 7 years or less) then you will want to hold off on any further decisions. When looking at new kitchen flooring, people find out very quickly how much they want a new kitchen. And by the time they get to renovating the kitchen, they either have to rip out the flooring (because they are changing the foot print) or they feel STUCK with a floor colour that dictates their colour scheme...and thereby feel cheated in someway because their floor doesn't let them chose the kitchen of their dreams. Whew. So much to be decided. All for a floor that probably won't work with the current cabinets/counters. Of course I could be wrong...especially if you have a stunning gray soap stone counter top. That would look STUNNING with the Pergo. But first, photos of what exists...just to be sure.

I would consider something painted. It's hard to make specific suggestions without pictures, which you can add in the comments. I would consider black painted shelving, cabinets to break up the honey oak, and provide some contrast.