p = Prompt()
while True:
p.prompt("> ", bottom_toolbar="toolbar")

after much investigation, it is caused by the output.erase_down() calls of the renderer.
I suppose for the prompt application, you only need to erase down to the bottom toolbar, so one solution is to override the erase_down method of the output?
EDIT, FloatContainer.write_to_screen is also responsible for the flicker when the prompt is near the bottom.