I'd change the direction! Would look better in a galley for it to run the length of the kitchen, rather than across the width, IMHO.
Here are some examples:
http://www.houzz.com/Wood-floor-changes-direction

Change direction for sure. Otherwise looks like it will only be about one board length from side to side and that doesn't look good in my opinion.

I disagree. Continue the same direction the boards run in the other rooms. Less choppy visually. Galley is a small space. You don't want to add any element that impedes the visual flow.

….I don't understand Advent Home Solutions' comment about looking like it would be only one board length side to side… I would think the opposite. Am I missing something?

I would run them to match the other room (left to right). It will look like its original and well planned out.

Goodness!! You have to look under the floor to see which way the joists go first! That's your first task. It is common for floor boards for run perpendicular, and believe me, once they are down, you won't notice it. Wood floors are so darned beautiful. It won't matter which way the boards run.

Run it horizontal. It would visually appear wider than it is.

Kmkane is right. If your on a slab it doesn't matter which way you lay them, but if you have a subfloor you must lay the perpendicular to the floor joists for a proper install.

I should have clarified. Flooring is 3/4" solid over a newly installed 3/4 plywood sturdifloor. Joists run parallel to existing mahogany direction, it's been a few years but I thought a flooring book by Peterson said that was acceptable over a a stiff enough substrate.

One more vote for leave them the same as the LR/DR. they will be across the kitchen rather than straight down the length of the room. This will help make the kitchen look wider. I have a galley kitchen and they can use all the help they can get to look larger.

Since you are getting such mixed responses, why don't you lay a few boards horizontally, then try them vertically, and see which one appeals to YOU the most.

Change direction, just make sure the threshold looks good.

I see two samples of tile. I would put tile in the kitchen. It will lighten up and expand the galley kitchen. The wood will match too much with the cabinets making the kitchen look dark and small.

The tile on left would work go with that.

Use the wood. Different flooring throughout a house can look dated. If laying either way is appropriate, go perpendicular. It will help make the room look wider.

I'm not sure if you have a basement or not but if you do, you should install flooring perpendicular to the floor joists if you have a sub-floor. Installing them parallel to the joist most likely the floor will sag between the joists and it will open up between the boards down the road or it could be worse.
We did a few jobs where customers wanted to run parallel to the joists, so we had to strengthen the sub-floor by adding a layer of plywood.

Appreciate all of the advice! Will let you all know what I go with shortly.

I apologize for bits I left out, such as
-I 'm going to guy kitchen down to studs and joists
-I'll have pros do electric and plumbing
-re-insulte, new subfloor, scrape and texture ceiling
-custom cabinets, painted poplar, probably sherwin Williams antique white
-stainless appliances with 36 inch French door fridge across (on the right side of pic) from current fridge
-widening this "doorway" substantially

With

Sushak,

could you please post an update?

going through same issues, except a much larger area would have a different direction. so frustrating. my head, and my floor people say do not change direction whenever possible. also, you are likely to lay a runner the length of the galley - nice☺️

same problem and they don't sell the wood laminate I have any longer. I decided to go with a luxury vinyl plank that has a stone look. It's a click together system. I'm trying to figure out which way to run the planks as well.

You can install your wood planks lengthwise into your kitchen, butted against the boards running in the other direction in the adjacent room. Been there, done that. No problem.