How can I print gears using very high resolution material like nylon
Proceeding with the expectation that you mean nylon rather than vinyl, there are a few options open for you. What resolution are you seeking? Layer thickness of 0.100 mm is quite good, allowing for ten layers per mm of part thickness, with infill adjusted as required.

If you've already determined that your printer will not print at the resolution required for your gear design, you would perhaps purchase a higher resolution printer. Of course, that may be an expense you would like to avoid.

If your parts count is small, you could consider to print samples of the parts to confirm fit, but not worry about strength and then use an online service to have them printed via SLS method.

Selective Laser Sintering places nylon powder on the work surface, then selectively melts the powder into a solid. Each layer when completed is covered with another layer of powder and fused to the previous portion (or not) until the part is complete. 

Because the un-fused powder provides support, there is no requirement for the model to have supplemental support structures. There is a requirement/objective that the part have "drain holes" in areas which might otherwise be solid. Any surface that entraps powder is charged to the purchaser as if the space within is included in the part.

An example would be a cube that can be printed as six square faces only. The cube wall thickness can be specified and if a drain hole is incorporated, the cost would be the volume of the walls only. No drain hole would mean the cube would be charged for the entire volume.

For gears, which are typically low profile/flat items, that's a minor consideration.

The same concept applies to SLA printing, which uses a laser in a vat of resin. If the model is a solid with no drain holes, the interior will retain the resin. It is possible that the interior can be cured with strong UV light and/or sunlight, but opaque resins would not accept this work-around, nor would it reduce the cost involved. Also note that SLA printed items would lack the necessary strength.

If farming out your parts is the direction you intend to travel, ensure the dimension stability reference in the vendor you use. Nylon sintered parts will shrink a known amount during the fusing process. The vendor should provide the appropriate reference, or the vendor should confirm that he adjusts the model appropriately for shrinkage.

I have one very tiny part constructed from SLS nylon and it's amazingly strong for such a thin wall. Nylon wears well too.