The TSA does allow fresh cut flowers through security checkpoints, as noted in their My TSA app:
You can bring fresh flowers through the checkpoint, but not in a container filled with water. We suggest wrapping the stems in damp paper towels and plastic wrap or foil to keep them hydrated while you travel.
Even if an item is generally permitted, it may be subject to additional screening or not allowed through the checkpoint if it triggers an alarm during the screening process, appears to have been tampered with, or poses other security concerns. The final decision rests with TSA on whether to allow any items on the plane.
Presumably you would have to put your flowers in one of the plastic trays in order to have them X-rayed at the checkpoint.
Note also that many people find strong floral scents to be obnoxious, and some people have reported adverse health effects when exposed to strong scents for prolonged periods of time. Regardless of the medical validity of these latter claims, it would definitely be a "hassle" if your seatmate objected to the idea of being in a confined space with some strongly scented flowers for hours on end. (I personally find the scent of easter lilies particularly obnoxious, and would at the very least be quite annoyed if I had to sit next to a bouquet of them.) Be prepared to change seats if requested, or to let the flight attendants keep your flowers elsewhere for the duration of the flight. A charming story about why you have the flowers with you would probably help in convincing the flight attendants to help you out, i.e., "they're for my girlfriend/boyfriend who I haven't seen in months" or something like that.
If you will have significant time during your layover, I would recommend you use it to revive the flowers in a container of water. If you can, bring a large cup that you can fill with cool water and put the flowers in it for the duration of the layover. During the flights, you will probably have to make do with wrapping the bases of the flowers in damp paper towels; there are some recommendations in this USA Today article about how to travel with cut flowers. (Summary: make sure the flowers have been soaking in water with flower preservative for a few hours before the flight, and then wrap the bases in damp paper towels soaked in the same solution of water & flower preservative, with plastic wrap and/or alumnimum foil around the towels to avoid drying and/or leakage.)