If you like red, there are gentler, browner reds / rusts/ spice colors that would blend better with the wood and floor. Another red over red wouldnt be that hard to do. As far as window goes (is there just the one?) a woven woodsy type of shade to relate to the wood elements or curtains with simple pat]tern incorporating reds/browns/whites.

I find it difficult to visualize another colour when the current one works but here goes... One option would be a warm ivory, pale pale yellow. Dial down the current colour a few notches. Another could be a terra cotta, burnt orange type colour. Dial up the gold a few notches. Not sure how that would fare next to the red in your kitchen though. Sorry I don't have actual paint manufacturers names and colours for these two options. Just took these pics from a House Beautiful book. I also thought a browny-pink could work. Very pale, too much yellow or grey in it to read pink. Something like Farrow & Ball's Pink Ground or Benjamin Moore's Silky Smooth. (On my screen, that's how they look. Might be very different in your space, with your lighting.) Depends on what direction you were thinking of going and how saturated you want your walls. Have you been checking out paint strips in the store? See what appeals to you there (blue? white?) and bring them home and see how they look in your space. Some will be a definite no, others might have promise.

Need wall color ideas for navajo white trim and doors

Walls in just the kitchen or the whole house? IMO to keep things simple do the walls in the same white as the trim just in a different sheen and if you are thinking an actual color then you need to show what is in all the rooms not just the kitchen