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I have no specific knowledge about this but suggest you post on the Vietnam forum rather than here.

In general, most countries are not likely to want to see someone become a citizen of another country and then ask for their old citizenship back – although the war is an exceptional occurrence that might be accepted as an excuse. Another question is if you want to give up your American citizenship, which might be required either from the Vietnamese or American officials. America does recognize dual citizenship now but with which countries and under which circumstances is relevant. Make sure you are properly informed before committing yourself.

I found this information from the US government site mentioned below:

A U.S. national may acquire foreign nationality by marriage, or a person naturalized as a U.S. national may not lose the nationality of the country of birth. U.S. law does not mention dual nationality or require a person to choose one nationality or another. Also, a person who is automatically granted another nationality does not risk losing U.S. nationality. However, a person who acquires a foreign nationality by applying for it may lose U.S. nationality. In order to lose U.S. nationality, the law requires that the person must apply for the foreign nationality voluntarily, by free choice, and with the intention to give up U.S. nationality.

Intent can be shown by the person's statements or conduct. The U.S. Government recognizes that dual nationality exists but does not encourage it as a matter of policy because of the problems it may cause. Claims of other countries on dual national U.S. nationals may conflict with U.S. law, and dual nationality may limit U.S. Government efforts to assist nationals abroad. The country where a dual national is located generally has a stronger claim to that person's allegiance.

According to Clause 1 Article 23 of Nationality Law issued 13/11/2008, Overseas Vietnamese who lost their Vietnamese nationality may apply for a restoration of nationality if they fall into two of the following cases:

- Repatriate to Vietnam;
- Have a spouse, a biological parent, or a biological child who is a Vietnamese citizen residing in Vietnam;
- Have made special contributions to the cause of national construction and defense;
- Their restoration of Vietnamese nationality is beneficial to the State;
- Have made substantial investment in Vietnam

Applicants can maintain their foreign nationality once a petition is approved by the President of the State.