There are a variety of techniques and materials, and a whole treatise (or two) could be written about it.
If you have a white or light-colored surface, just plain used motor oil is best. It has extremely fine particulates and flows smoothly. Adding tempera paint to clean oil will let you change color, so for example if you have a dark surface, use white tempera paint. But it is very hard to mix and filter this paint-oil mix well enough to not have it be somewhat gritty. For gross flow visualization, that may be just fine, depending on your purposes. But the grit will trip a laminar boundary layer early, so it is not useful for visualizing laminar separation, laminar bubbles, or transition.
There are several application techniques too. For streamline visualization, just paint it on over the whole surface. One way to produce really dramatic visualizations of separated flow is to put a stripe of paint-oil along the forward portion of a surface, or a row of dots, and then fly. The paint-oil will flow back, but can not get inside the separation zones, and so will leave those areas completely uncoated. With highly 3-D separation (such as a vortex sheet formation) you may see the oil run around the separation point and fill in behind it, perhaps showing surface vorticity, or creating a number of interesting patterns.
If your goal is to just be sure a surface is aligned to the flow (zero angle of attack) then coat both sides and then check that the attachment line is right on the leading edge. From the leading edge back, it is unlikely that the 'upper' and 'lower' surface will look much different for something like a strut fairing or wheel pant, even if it is at some angle of attack, because there is little if any flow separation, but you will see the attachment line move off the leading edge.
Now the biggest challenge for flight test. You put the stuff on on the ground, and then taxi, take-off, climb, cruise, descend, and land. What part of that flight gets imprinted in the oil flow patterns? It depends. If you put enough on to keep it wet during the whole flight, then it will be biased toward the end of the flight in terms of what has the most influence. Flow character from early in the flight will get 'erased' by additional flow later in the flight.
For some things, you may not care. Certainly landing gear strut alignment to the flow is somewhat sensitive to angle of attack (speed).
Another challenge is gravitational effects on the oil before, during, and after the flight.
A couple of choices: If you put a thin paint-oil mix on, and cruise until it actually dries, then the patterns of flow will be more or less preserved at that flight condition and not corrupted by the landing phase of flight. If you can mount a camera that can see the area of interest, you may be able to record the flow behavior at the desired flight condition, or maybe even more than one condition.
Interpreting results is challenging and interesting, and especially for highly 3-D flows, you can not assume that the flow on the surface is the same as the flow a short distance up off the surface. Examples are spanwise flow on swept wings, especially on the underside in areas of fairly slow streamwise flow component, and areas like the belly just behind the cooling flow exit, where you can very likely see vorticity/recirculation on the surface, but a short distance up off the surface the flow could be perfectly-well organized.
Getting the oil viscosity what you want can also be tricky, and depends on what you want to visualize. If you want to make a pigmented coating that will 'dry' at some point in the flight, then thinner oils are better. If you want to keep everything wet and flowing, heavier oils are better. You will likely find that in areas of high surface shear stress, like the forward portion of an airfoil, the coating may be wiped fairly clean. That is a useful result in itself, it tells you the flow is attached and high velocity near the surface. All that oil has to go somewhere and it will thicken in areas of lower shear stress or lower velocity. Interpreting sudden changes in residual oil can be tricky - it could be transition, it could be a laminar bubble, it could be separation. It takes experience with these to recognize tell-tail signs of each.
I will follow with a few stories, and answer what questions I can.
Oh and full disclaimer - I take no resposibility for whether oil or paint stains or discolors your airplane. I can not promise that a good coat of wax will prevent it, although it seems like it would help, but it may prevent the oil from wetting to the surface, and give different/spurious results.