FlashBack can record at whatever quality your screen is capable of displaying, including HD or 4K qualities.
For example, if your screen is set to a 1920 x 1080 resolution and you record the fullscreen, the saved recording will also be 1920 x 1080, which would be HD.
If only a region of the the same 1920 x 1080 screen is recorded, the saved recording will have a resolution that matches the size of the selected region. If that resolution is smaller than 1920 x 1080, it won't be considered HD.