It only has 3 colors on it's wings, a rainbow isn't 3 colors, it's 7. This also makes a couple of it's pokedex entries incorrect.
It is said that when it flies its huge wings to create bright, colorful rainbows. The rare few who bear witness to Ho-Oh are promised an eternal happiness.
This alone may be why it is called "Rainbow Pokemon."
Legend says that its body glows in seven colors. A rainbow is said to form behind it when it flies.
Source I Source II shows Ho-Oh flying towards a rainbow it most likely created.
Hopefully I've Helped!
