Unlike other games, plants in Flower Garden don’t grow automatically on a timer. Like real plants, they need some care on your part.
The best way to take care of your flowers is to give them one good watering until the water meter is as far right as possible (without going into the overwatered area). You’ll see an initial growth spurt, but most likely the flowers won’t bloom yet.
Tap on the tag on the pot and you should see how long it will take for the pot to dry. Come back to your garden before that time and give it another full watering.
Repeat that and you’ll have blooming flowers in no time.