Hi Marci, you ask a fantastic question! You're right, a giant column of air, miles in length, extends on top of all of our heads at all times and it is heavy. That column of air and the whole atmosphere in general gives the earth its characteristic air pressure.
You can think of pressure as a force divided by the area over which it applied. In the context of the column of air, that force is the weight of all of that air and the area is the area at the base of the column. Air pressure is super important and has very real consequences whether it be the temperature at which water boils at high altitudes (like in the mountains) or what happens if someone opens the door of an airplane while it is flying. So, to get back to your question, why doesn't the air pressure crush the tiny flower? Well, the simple answer is that the flower evolved to grow in that pressure. Your question is the same as asking why humans can stand up given the amount of pressure we experience.
Basically, the organisms on Earth evolve to endure the pressures that they are subjected to. You can extend that to look at some of the sea-dwelling creatures that live at the bottom of the ocean. They have evolved to survive in pressures that are over 1000 times higher than those that we experience on land. Any human or tiny flower would be destroyed by those kinds of pressure. However, they survive through specific adaptations that have allowed them to live comfortably in those extreme environments.
So, to summarize, organisms evolve to survive in the pressure that they experience every day. If an organism is taken out of the pressure that it is adapted to, it is likely to have a lot of trouble and could potentially die.