Fullscreen Flicker Problem

I think we need some more information.

Is the application single or double buffered?

I guess it is "double" b/c:

In the GLUT version, I am calling the following:

glutInit(&argc, argv);
glutInitDisplayMode (GLUT_DOUBLE | GLUT_RGB);
glutCreateWindow("test");
glutFullScreen();
glEnable (GL_BLEND);
glBlendFunc (GL_SRC_ALPHA, GL_ONE_MINUS_SRC_ALPHA);
glClearColor (1.0, 1.0, 1.0, 1.0);
glShadeModel (GL_FLAT);
glutDisplayFunc(display);
glutReshapeFunc(reshape);

then:

void reshape(int w, int h)
{
glViewport (0, 0, (GLsizei) w, (GLsizei) h);
glMatrixMode(GL_PROJECTION);
glLoadIdentity();
gluOrtho2D(-512.0, 512.0, -384.0, 384.0);
glMatrixMode(GL_MODELVIEW);
glLoadIdentity();
}

void display(void)
{
if(once == 1) {
glClear(GL_COLOR_BUFFER_BIT);
once = 0;
}
// DRAW STUFF HERE
glutSwapBuffers();
glutPostRedisplay();
}

The non-GLUT version is similar, based off of NEHE examples (
http://nehe.gamedev.net/lesson.asp?index=01), set to be ORTHO2D and with the same display code.

I guess the problem is the following:
If you use Doublebuffering, you have 2 buffers which are alternately shown on the screen.
Since you are only clearing one of the buffers, the other one still contains the old content, i.e. the desktop.

You should take a look at "Accumulation Buffers". They exist just for this purpose. Additionally, they deal with Color Scaling and often have pixel formats with a wider range to avoid saturation.

Yonibear: sounds good. accum buffer isnt hardware accelerated on most hardware. try to clear several first frames . not only the first.

Ok, but clearing the buffer several times at the start won't solve the problem. On each buffer the frames drawn to the other buffer will be missing.
Additionally, the color buffer amy always be corrupted, for example when the OpenGL window is overlapped by another window.

The right way would be to implement some sort of manual double buffering by rendering to a Framebuffer Object. FBOs are always single-buffered, so you can accumulate the scene on them. After that, you should render the texture attached to the FBO with a fullscreen quad to copy it to the back buffer.