Steve, I have merged your "Bottling Modified Sauce?
" with the original "How do I preserve this chili oil sauce
" since it is an add-on question (a continuation of a previously asked question) and not a really a new topic.
To answer the overall question simply - it's not recommended for home canning
. Of course, if you are a food chemist, have a lab, know what you are doing, got pressure canning equipment ... yeah, you could. But, if you had all that you wouldn't be asking us, would you?
Yes, you can buy flavored oils off the shelf and they can last for several days at room temp on the table with no problems. They have been "commercially" processed - and there are many facets to that processing.
If you're interested in doing a little research on the subject - try the National Center for Home Food Preservation
website to get you started.