I wrote the following before you showed your floor plan idea. The right triangle trick described is based upon running the flooring at right angles to the room to room threshold. If you want to be perfectly parallel to the room to room threshold then you can either start at the threshold and run the flooring in both directions toward the far walls. Otherwise make your start run line by measuring over from the room to room threshold to near the starting wall. After that follow my latter steps for dealing with an uneven wall.
The chalk line when stretched between two points will snap a straight line. If you want the rows of flooring to be square to the threshold going into the adjoining room then you do not want to measure from the wall to establish where to place the first courses of the flooring. Here is what you'll have to do.
1) Layout a straight line fully along the threshold area that will be at right angles to the flooring runs. This does not need to be exactly at the threshold edge but can be offsetted parallel to the threshold edge. It is beneficial is this line can be as long as possible say either three feet or six feet in length.
2) Near one end of the threshold line temporarily nail in a small but sturdy nail and leave it stick up about one inch or so. It can be handy if this nail is placed at the end of the line nearest to the starting wall for the flooring.
3) Measure along the threshold line from the first nail for exactly 3 feet (or 6 feet) and place a second nail into the line at that point. Get this as close as possible to exactly the right distance.
4) Now place a string over the end of the first nail and stretch it out approximately along the starting wall for a distance of more than 4 feet (or 8 feet). Use a string that has little or no stretch when it is gently pulled taut.
5) Measure from the first nail along the taut string and make a narrow dark mark on the string at exactly the 4 feet (or 8 feet) mark.
6) Now hook a tape measure over the second nail and draw it out toward the area where the string is marked. Move the string back and forth till the mark shows at exactly the 5 feet (or 10 feet) mark on the tape measure. Note the exact intersection point under the string where this point is located. (You could install a third nail at this point if you wish). The three points where the nails are located will describe a large right triangle.
7) You can then snap or draw a straight line through the points where the first nail and third nail are located. This line will end up being parallel to the first run of your flooring.
8) Next measure over from this line over to the starting wall so that you can accurately locate a second line that is nearer to the wall. With good luck you will hopefully be able to note that the wall parallel to the line all along its distance. :-)
9) Follow the flooring manufacturers directions on how to measure and mark for the first flooring run from the wall. This is usually the width of one run of flooring plus the expansion gap width. If the wall is relatively parallel to the line and only has moderate variations you can let the expansion gap eat up the variations. Some places the gap will be a little less than the recommended amount and sometimes a little more. If the wall is very uneven or not particularly parallel to the reference line the you'll have to mark your first run according to the point that the wall is closest to the reference line.
10) Once you have measured out and measured where the tongue edge of the first run is to be located you can snap or draw a line between the marks for the first run. The idea is that this line be as close to parallel to your nail one to nail three reference line as possible.
11) If the first flooring run line has more variation than can be "buried" in the expansion gap then you will have to cut some flooring pieces that get glued into the groove side of the first flooring piece to come up to the wall minus the recommended expansion gap. Clamp and let the glued pieces dry well before installing the first run.
12) Installing the first run wants to be done with surface nailing down into the sub floor. This is necessary so that you can keep the flooring right even to the first run line. The idea is to surface nail close to the wall so that the nail heads will be covered by any baseboard and base shoe that get installed after the floor is finished. For the uneven and non-parallel wall you can now see the importance of the step to glue in the filler pieces. The reason being is that this row of surface mounted nails may need to be through these pieces in order to be close enough to the wall to be hidden by the base mouldings.
13) Once the surface nails are securely installed the tongue side of the first run can be nailed. It is highly recommended to pre-drill these nail holes at the angle into the tongue and then pound in the nails with a hammer and set below the tongue surface with a nail set. Use extreme care that this installation step does not tend to crowd the first run over off the starting line. If you see this happening you may need to install additional surface nails along the wall.
14) Finally you are ready to install the next flooring run.