If you hire a flavor development company to create flavors, who are the end owner of the finished product?

If the flavors have been in use (probably meaning on sale in a soda, or pop depending on your location) for more than a year without a patent being filed, then there can't be any patent issue. A recipe won't be covered by copyright, so you wouldn't have to worry about that. Ownership of the flavors is almost certainly covered in the contract, which can't be found. It would be best to have the company sign off, to cut off any possible issue that might come up if the contract is found.

Presumably you hired this company to create flavors that your company would incorporate in your products and own free and clear, and this was not a license.

Since the company has told you it doesn't care what you do with the ingredients, which apparently you have been using without their objection for these past years, it's unclear why this company won't sign anything. The best way to ensure that they never claim ownership or use rights is to get them to sign a release or quitclaim to these flavors. If they won't do that, you can at least send them a letter confirming your understanding of the situation, via registered or certified mail or Fed-Ex so you can prove receipt, and then you'd have a "laches" argument through their activity over the passage of time that you relied on them having no rights and will continue to do so.

Disclaimer: Please note that this answer does not constitute legal advice, and should not be relied on, since each state has different laws, each situation is fact specific, and it is impossible to evaluate a legal problem without a comprehensive consultation and review of all the facts and documents at issue. This answer does not create an attorney-client relationship.