Smoke: it's a solid that will deposit everywhere and possibly damage the moving parts. Within this option, I'd prefer soft and lubricating solids, like graphite and molybdenum disulphide, which are both available as very thin powder like 50nm. Their powders float in air for long (and are dirty for real), so you only need to let them fly, for instance by shaking the tank.
Though, depending on the flow to measure, I wonder if there are better methods. If the measured gas bubbles through water in an inverted test tube, you observe <1cm3 which can accumulate over hours if needed.
Really small flows (rather leaks) are measured with helium (which leaks much worse than other gasses). Put helium at one manifold side, clean air at the other, measure the helium concentration resulting from the leak. That one is more sensitive than what you need, but suggests a method: have a remarkable gas at one side, clean air at the other, measure the concentration over time.