Chrysanthemum
The chrysanthemum is an important symbol for Japanese people as it represents the sun. The flower and its petal itself is considered to be a natural perfection. A single chrysanthemum petal is often placed in the bottom of a wine glass to represent good health and longevity.
In the west, if we don't have Chrysanthemums we can substitute it with Dahlias(bottom picture). The Dahlias are also shaped like and would compliment any arrangements nicely.
Iris
The iris is a symbol of heroism and nobility in Japan. The word for iris in Japanese is "shoubu." Irises are thought to offer protection from natural calamities such as storms and typhoons.The idea that irises ward off evil came from China to Japan.
If Iris(top) is not available Orchids(bottom) can be used as a substitute. Orchids are the ideal substitute for Iris because of the variety in color and also the shape is almost similar.
Peonies
Peonies originally were from China and came to Japan with Buddhism by the eighth century. Peonies are often used in ikebana because it symbolizes wealth and prosperity. In ancient times, only the rich and middle class families can afford to raise peonies.
If Peonies(left) are not available, Carnations(right) are the best substitute. In my opinion the best substitute for Peonies are Carnation. The shape of Carnation flowers bear striking resemblance to Peonies. You can also use Roses.