Flower hybrids in Animal Crossing: New Horizons are unique combinations of two different colored plants being turned into something new. You only obtain these hybrid colors through cross-pollination. A unique combination you can create in New Horizons is blue roses.
Before you start to create a hybrid flower, you need to place two plants next to each other. There needs to be at least a space between them where the hybrid flower can grow.
Now, you need to do a handful of things before you can make blue roses, though. The first thing you need to do is create a pair of hybrid red roses. You can only make blue roses by combining a hybrid set of red roses, not the ones you can traditionally find on other islands. They must be hybrid red roses. To make a hybrid red rose, you need to combine orange and purple roses, which are also hybrids. You can combine regular red and yellow roses to make orange, and white and white or white and yellow roses to make purple.
After you have your orange and purple roses, go through the same process you normally would creating a hybrid plant with the orange and purple to create a hybrid red. You need two of them. Once you have your two, place the hybrid reds next to each other and wait for them to create their hybrid combination. You should see a set of blue roses between them after a few days of watering.
You can create a variety of different color combinations in Animal Crossing. Not all of the flowers have the same combination, though, so make sure to experiment with every flower you obtain in the game. It can take several days for them to grow, so take your time with the process.