Transitioning from dining room to living room does decor need to flow?

If the rooms are connected - they should flow in to each other - as all rooms should that connect.

Yes, if they are adjoining. You can use the same colours only differently though............

This is a nice article on this:

http://www.hgtv.com/design/decorating/color/connecting-rooms-with-color

my dining room and my sitting room have pocket doors between them, but these are always open so there is a wide doorway between the rooms. The painted floor is the connector and also the wall color. But just in general, you are decorating your home so there will be a "connection" between all your rooms as your choices will be similar in each space you decorate.

Yes, use the same colors, but in different quantities, especially if it is an open floor plan. My dining room is separate from the rest of the house, so, although I have used the same basic colors for flow continuity, it is decorated with a more formal look