Does our solar system have enough bodies in orbit to appear to twinkle to another distant solar system viewed from the side?
While objects blocking the sun may have an effect on the twinkle if viewed on another planet, a twinkle is mainly caused by the effect the atmosphere of a planet has on the light, or something interfering with the light that is passing to your eyes.
From Wikipedia's article on Twinkling:
Twinkling, or scintillation, is a generic term for variations in apparent brightness or position of a distant luminous object viewed through a medium. If the object lies outside the Earth's atmosphere, as in the case of stars and planets, the phenomenon is termed astronomical scintillation; within the atmosphere, the phenomenon is termed terrestrial scintillation. As one of the three principal factors governing astronomical seeing (the others being light pollution and cloud cover), atmospheric twinkling is defined as variations in illuminance only.
Stars twinkle because they are so far from Earth that they appear as point sources of light easily disturbed by Earth's atmospheric turbulence, which acts like lenses and prisms diverting the light's path. Large astronomical objects closer to Earth, like the Moon and other planets, encompass many points in space and can be resolved as objects with observable diameters. With multiple observed points of light traversing the atmosphere, their light's deviations average out and the viewer perceives less variation in light coming from them.