There was a recent kitchen thread discussing what flooring went with white cabinets and gray counters. The OP had red oak flooring throughout her house and couldn't decide how it would look in the kitchen. It's kind of the reverse of your problem, but there were pictures that showed white and gray looking great with red oak. Here is a link that might be useful: White cabs/gray counters; forgot about the flooring!

We are installing a QS red oak floor and QS white oak cabinets. I guess we are doing the opposite of what you are proposing... The floors will just be sealed with no stain and the cabinets will have Miniwax red oak stain. We wanted the wood to complement each other but definitely be distinct so they didn't "blend into" each other.

The Elephant in the room needs to be talked about: the age of the kitchen cabinets/counter tops/backsplash. This kitchen is clean and functional but dated. The counter tops are tile and the floors are laminate and the cabinets/boxes are dated as well. That means the kitchen is going to be ready for a renovation sooner rather than later. I mean in the next 7 years or so. Which means you need to sit down and do some HARD thinking. A kitchen renovation OFTEN (80-90%) changes the FOOT PRINT of the kitchen (the cabs are ripped out, holes in the floor are patched, etc). That means whatever floor you put in TODAY is going to need changing or a SERIOUS repair tomorrow. Right now you are trying to get a "refresh" of the kitchen without looking down the road at the FULL RENOVATION. That can get you into a bit of trouble. In your situation, I HIGHLY recommend that you sit down and plan out the next 7 years of your renovation life. Yes. Seven years. No. I am not kidding about this. To do this type of planning you have to have an END point. You need to know the FINAL look of your kitchen so that you can work towards it one step at a time. That means you need to have picked the COLOUR PALETTE for your kitchen before you lift a hammer. I like to see homeowners shop around for samples of things they like and then put those things into a basket in the trunk of their car. They will then keep the basket handy for when they see a 'GOOD DEAL' somewhere. If the deal fits the colour palette PERFECTLY, they you purchase it. If it doesn't, then you move on and save your money. Whew. But to answer your question, your wish for gray/white floors with red oak is going to be EXTREMELY tricky. Gray floors can have a peach/green tinge to them. And that will be a MASSIVE clash with orange-brown cabinets. You are welcome to put the floors in the house and kitchen, but BE PREPARED to HATE what you see. That's OK. Hate is an excellent motivator. It will move your 7 year renovation time line forward to include a 3-5 year time line. But your choice will push you towards a new look very, very, very quickly. Before you do that....please make sure you have a path set out to get to your final destination. Once you pick new floors, the destination will come faster than you ever thought possible. You will notice your inspiration kitchen is white on white on white. It is airy and sophisticated transitional/modern design. Your kitchen is not. As cute as it is...it is not. Please take a moment to investigate WHY you like the photo so much. It may not be "just the floors". You may LOVE the look that has been created. And that means a total redo of your kitchen.

Sorry but a good flooring professional will do the colour patches on your own floor and not just on samples. And they then apply a single coat of your finish (and sealant) over your choice. You live with it for 24-72 hours and then tell them. Sigh. Are you using a stain? Stains do not always need a sealant. You have listed sealants but not a finish. I know you said Bona, but bona has many finishes...some carry a yellow tone...but many do not. Which FINISH are you using? Bona Mega? Bona Traffic? Bona Traffic HD? Which finish are we using? Yes. It will make a difference. And not all stains accept sealant (it all depends on who's stain line the refinisher is using). To reduce the red in the red oak many people use Jacobean (minwax/duraseal name) because it has green tones in it. Do you have a pic/sample of your cabinet choice? Is there a reason why the floors are being done before the cabinets are installed? Usually floors are done last. And just for fun...there are multiple types of 'walnut' out there. Some are red/brown. Others are brown/mushroom/caramel and then there are the 'exotic' woods that have nick-names like Brazilian Walnut...etc. Do you have a photo of your cabinets?