It would help a great deal to know what your "flat screen HD TV" is (make and model). If you bought it in the U.S. recently, it has the tuner (and the antenna jack) for the new over-the-air (OTA) digital channels.
If it's an older "digital ready" HD monitor with no built in tuner (commonly sold in the U.S. a few years back), it will need some outboard device to receive channels, such as a cable or satellite set top box.
For OTA, the low cost converters purchased with a coupon in the U.S. will work with your set, but they also work with any old analog set. In fact, that's all they do--their output is standard-def analog, not HD. You won't like it.
With a no-tuner HD monitor, you might consider something like the DTVPalDVR (see the link), which receives the OTA channels and outputs HD to your set, plus it has a built in hard drive recorder. It's pricey, but it will give you the full benefit of an HD monitor. Just be sure that your set doesn't already have a built in digital tuner (look for "ATSC" on the tuner description if it has one).