To 'unload' your bitmap, there are some other things you have to do. There is no such thing as 'clearing 1 bitmap without clearing the screen', at least not in the way you want to do it.
In this case I think you actually do want to clear the full screen.
You want something like this
void SplashScreen::loadContent() {
image1 = al_load_bitmap("SplashScreen/image1.png");
image2 = al_load_bitmap("SplashScreen/image2.png");
//clear screen
clearScreen();
//draw your splash
al_draw_bitmap(image1, 0, 0, NULL);
//display it
al_flip_display();
//wait for 2 seconds
al_rest(2);
//fresh new frame
clearScreen();
//draw this second image, I don't know what this is
al_draw_bitmap(image2, 0, 0, NULL);
//display it
al_flip_display();
//wait for 2 seconds
al_rest(2);
//fresh screen again
clearScreen();
//display it
al_flip_display();
}
The general drawing procedure for a game goes something like this
1-clear your screen
2-draw everything you want
3-flip the display
4-wait a few milliseconds
5-restart back at 1
This way you get a fresh screen at the start of each frame. The only difference for a splash screen is you wait 2 seconds, not a few milliseconds
At the end of your program, call destroy_bitmap to free the resources.