Hi Matt,
Is this the kit you have?
http://www.harborfreight.com/cpi/ctaf/Displayitem.taf?itemnumber=47791 
I had one of these bottom feeder sprayguns (albeit a Badger) a while back. Here's what I'd suggest:
1) if the problem exists between the pot and the tip (seemingly since there is airflow from your source) take these pieces apart and blow air through each individual part, thereby checking for the blockage.
2) if there is no blockage, it is possible that your source of air isn't strong enough. And on that note you haven't told us if you're using a can, tyre, or compressor.
3) try shooting/spraying water through the A/B, if that works, then it could be a case of your paint mix being too thick.
I must admit, I've never oiled a A/B, and certainly not a basic one like this, so I'm not sure if that may have had some sort of negative effect.
Just a small heads up about the Harbour Freight A/B products: Being unfamiliar with the brand, I did a quick search and unfortunately the Harbour Freight airbrushes appear to be somewhat lacking in the quality department. I hope not, but this seems to be one of those terrible "you get what you pay for" situations, but mind you, at less than $10 for the A/B kit who could blame one for giving it a go.
Rudi