Correct direction of flooring
Yes, I think you are correct, having two kinds of flooring that look like wood laid at right angle to each other could look odd. 

However, having two different appearing wood floors could look odd too. If you can’t match the living room flooring EXACTLY, I’d choose a different style, color, texture, etc. of flooring in the kitchen. 

The kitchen is a totally different use than the living room, which gives you an opportunity to change the flooring. 

Often, when we design, we want to “define” each space separately. That is to say, we want to give each space it’s own character. Changing floor color, texture, etc. is one way to do that. 

Consider a tile floor in the kitchen.