My U.S. company is owned by a Hong Kong limited company. If we transfer money from our Hong Kong account (parent account), to our U.S. account (subsidiary account), are those proceeds taxable?

I guess it depends; say,it can be Intercompay loan, then, perhaps, you need to first determine if the loan is a) long-term in nature or b) short-term in nature. Under U.S. tax law, the IRS may impute additional interest in case the rate of interest on a loan from the Foreign parent to its U.S. subsidiary is below the market rate. The effect is that the subsidiary would receive a deduction for the additional interest imputed and the parent would recognize interest income for the same amount. This effect could result in either positive or negative tax consequences depending on the facts. If it is determined to be long-term, you will record the change resulting from foreign exchange translation in equity , otherwise the changes will be recorded as gain/loss through the income statements of the US sub; You need to review the loan governing documents first. Money flowing off-shore to on-shore is often treated as a "deemed dividend" and taxable as such. Often this result can be avoided if the monies put into the sub are carried as capital. US law requires businesses to prepare and file an information return when cash amounts exceeding $10k are received (Form 8300).
Note; Under U.S. tax law, interest paid on a loan from a company's foreign parent generally is tax deductible by the U.S. sub company. On the other hand, payments made by the U.S. company to its foreign parent in connection with its stock is considered dividends, to the extent of accumulated Earnings & Profits (E & P), and are not deductible by the U.S. company. In either case, the amounts received by the parent company are subject to a 30% withholding tax. Payments to the parent in the form of interest rather than a dividend will, therefore, reduce the sub company's U.S. tax.
Under U.S. tax law, debt may be recharacterized as equity if the company's ratio of debt to equity is not considered reasonable. Both the IRS and case law have developed criteria for determining if the debt to equity ratio is reasonable. If the U.S. sb company is too thinly capitalized (i.e., too much debt and too little equity), payments considered as deductible interest on debt may be recharacterized as a nondeductible dividend

much appreciate the detailed feedback. The issue is a bit more complex than I expected. I'd be interested to see if it can be categorized at capital...which is really quite accurate as we have a lot more expenses in the U.S. than we do in HK. Time to find an expert in Denver to help with this.

vbery good idea' you can contact an IRS Enrolled Agent/a CPA doingn taxes in the local area for your fed/state taxes