That was intended as a joke, Ireland. Lighten up, please?

Trick question. US military advisors are US military. The first US POWs in Vietnam were captured in 1954.

So, Mad Jack Percival aside, the US helped fund France's attempt to retake Vietnam as a colony post WWII. The US sent it's first few advisors in 1950. After Ho Chi Minh defeats the French at Dien Bien Phu, the country is partitioned by international conference in 1954 (though the US wasn't a signatory). US takes over in 1956, installed Diem as premier and set up MAAG (Military Assistance and Advisory Group). By the time Kennedy takes over, there are around 700 "advisors" in Vietnam.

Diem's crackdown on Buddhists and nationalists begins, many South Vietnamese flock to join the ranks of the NLF, Diem falls when the US backed the generals/gangsters' coup. The generals/gangsters got overzealous, and started to overthrow one another, leading finally to nine coups, and tremendous political and economic instability. US military involvement goes from the 500 or so US military dispatched to Saigon in the mid-50s, to approximately 25,000 at the time of the 1964 election. By the end of '65, there will be almost 200,000.

Now, what does this have to do with your father being killed while in service to the British army in Vietnam in 1967?