My family room is painted in Restoration Hardware Saffron. The already painted huge fireplace was repainted in RH Butter and all the trim is RH Buttermilk. I love the colors, but the kitchen can be seen from one side of the family room and the front door/entryway can be seen from the other side of the family room. So the question is, What color(s) can I paint these areas so that there is flow and the colors don't clash? I have read that the saffron is about the same color as Benjamin Moore Chestertown Buff.

Those color combinations are so perfect because they are neutral. You can choose your favorite color(s) and go with it. Just about everything will look good.
I chose black with mine, but then I wanted a dramatic effect in that particular room.

Welcome. If these are indeed neutrals, the options are broader in adjacent rooms. Lighting, flooring and furnishings should also impact your wall color choices. Cross pollinate colors room to room w/ variances in patterns, hue values and predominances to unite the spaces and create the flow you seek. FYI, it's always easier to achieve this cohesiveness if you use a print as a springboard to establish your scheme and give color cues to incorporate in adajacent rooms throughout your public spaces. A print will take the guesswork out of a pallet which can then be carried to a degree, onto adjoining spaces.

I would go with either the Butter or Butter Cream (the color between Butter and Buttermilk). Another option is to go with a deeper color like in the brown or burnt orange colors, depending on what kitchen cabinets you have. They are pretty neutral colors so you have a lot of options. Just depends on how well you want everything to flow.