Mahogany is inherently red. You may get to brown but there will always be red undertones at the least.

Using stain with green undertones, like DuraSeal Coffee or Ebony, will counter the redness somewhat. If that doesn't achieve your goal, the wood could be bleached before staining.

I love the color of your floors, and I wouldnt change them at all.

I'm seeing bevelled edges. That means these floors *might be engineered hardwood and not solid. There are solid floors with bevelled edges (solid factory finished are out there) but the most common visual for a bevel is engineered (not always...but mostly).

Before you try to figure out the colour, you will want to find out if a full sand and refinish is even possible. Please check a cross section of the floor. This is easily viewed by removing a floor vent. Have a look at the product. If you see multiple layers (kinda like plywood) then you have engineered floors. If that is what you have, then you will want to measure the TOP layer. It MUST BE 3mm or thicker to achieve a full sand/refinish.

Now the other thing: the finish itself. These are factory finished floors...that part is certain (the bevel together with a NEAR PERFECT FINISH gives it away...). The floors look to be in AMAZING shape (not just good...but perfect).

Your kitchen remodel will probably involve a change in footprint, am I correct? That means the remodel will go 'down to the studs' and then a full rebuild will occur. A foot print change means you will need some extra wood to fill in where some of the cabinets currently sit.

Whew! This could mean a full remove/replace the wood THROUGHOUT the home. Please look at your layout and figure out how MUCH more flooring you would need. And then check to see if you have extra boxes of the floor you have. If you do not, you may have to choose another floor for the kitchen. If you want to keep wood throughout, this may mean a whole new budget item and a whole new timeline for your remodel. And a shocking new time line.