Images: Blue bachelor buttons, white gladiolas and red nasturtiums.
Patriotic display gardens come and go in popularity. I've seen some really amazing displays over the years and always enjoy the effort. Some examples:
A circle flower bed, divided into pie shaped pieces. Alternating red and white petunias, a round center of blue dwarf veronica and the whole bed outlined with gold marigolds. It was on a slight embankment. It was stunningly beautiful.
Another bed was rectangle and also situated on an embankment. They had spelled out their family name with marigolds, set the background in white petunias and edged in red petunias.
Simple stripes of red, white and purple/blue petunias look pretty and get the message across.
Low growing annuals make the best plants for displays where form is important.
If using petunias, make sure you don't use the Wave or vining varieties.
There is no true blue petunia nor is there a bright gold. There is an almost blue purple and a very light yellow.
It's important to pack your plants pretty tight even in the beginning so the "bed" or canvas is completely covered.
If form isn't important and the mix of the colors is the end goal, using taller or spreading plants will work if they all have the same height and behavior.
A good place to have a small display is a container garden. Using red, white or blue pots with contrasting flower colors is also pretty.
Some like the use of gold as an accent to the typical three.
If a hillside or embankment isn't available, it is possible to use height for a visual effect. Use tall plants in the middle (perhaps red canna), surround in the middle by blue bachelor buttons, and the outside lowest layer white alyssum. Something like this looks pretty surrounding a flag pole.
You may choose to use hardscapes for the patriotic effect: flags, bunting, yellow ribbon, wreaths and more. Then, add a background of perhaps one color of flowers.
Colored stepping stones or colored glass can make a bright statement. An example would be a blue gazing ball set in the middle of red and white petunias.
A mosaic or specific design takes weekly upkeep to make sure the plants are always full and the shape is defined all summer.