storing crispy fried onions
There are three things to watch out for regarding long-term storage: moisture, oxygen, and light.

Too much moisture and your product is potential food for spoilage organisms. If you are making onion strings, it is likely that the frying process will have already dealt with that and the moisture is down to an acceptable level. Larger onion rings might be a problem as the onion pieces would typically have a lot more moisture - the reason that those thick crispy onion rings from the burger joint you put in the refrigerator are never as good the next day. I have been unable to find an actual number for this value for percent moisture, but if you have the equipment to measure this as a number it is highly likely that you would not need our assistance to answer your question.

Second, are two factors that impact your product going rancid: light and oxygen. If you are frying in any oil that is less than fully saturated (pretty much anything other than lard or fully hydrogenated vegetable oils), you have double-bonds in the fatty acid chain susceptible to oxidation or UV degradation, and in sufficient quantities the resulting compounds are highly unpleasant (butyric acid being one example).

Rancidification wiki link

You will need to either 1) replace the oxygen in the container with something like dry nitrogen, or 2) put an oxygen scavenger into the container (those little "do not eat" packets in some bagged foods you purchase). Also, the reason that many potato chips are sold in mylar bags is to prevent spoilage related to light exposure, so using a brown glass bottle would be better than clear, although not entirely protective.

I do not know that "canning" would be a great idea, as surrounding the jars with a water bath would risk introducing more moisture and there may be insufficient water remaining in the jars to purge the air by boiling off, which is how the vacuum is formed with canning. It might be better to use a canning jar in a vacuum chamber (yes I have one in my kitchen, but I'm not normal). The side effect of this would be that prolonged exposure to a vacuum would remove additional moisture by boiling off residual water, and you could then refill the chamber with an inert atmosphere (the dry nitrogen) afterwards, so less of a need for the little oxygen scavenger packets.