What flowers will you be growing? In all honesty I would be surprised if you could keep them to a grid style planting. At least some of what you grow will self seed and spread.

If you are looking at packages of seeds then you have the information you need for how many plants per square. Just look for the shorter of the two measurements in the usual statement "thin plants to x inches apart in rows y inches apart." The x number is the one you need, and the SFG method gets rid of most of the thinning and all the weed filled rows. ;)

As far as laying out the squares goes you will want to find out which plants will grow tallest and put them on the northern edge of the bed, putting the shortest flowers on the southern edge. For the best plant growth you want an arrangement that gradually rises from south to north. That arrangement should give you the best productivity for your cut flowers, then again you may just want to think about the color of the flowers you plan to grow and make a pleasing design in your imagination or on paper with some colored pencils, crayons, etc. to envision a bed that may be a little less productive but more appealing, to allow you to better enjoy your flowers before you cut them. The only caveat here is that the really tall, bushy, plants will shade out smaller things behind them almost completely and small flowers that don't get enough sun probably won't flower much, although varieties that don't like too much sun may do well shaded behind your bigger plants.