How did he flee:

His Jewish father Louis lost his teaching job. But he defied Nazi segregation sometimes too, sneaking into soccer stadiums to watch matches. This, too, would often result in beatings from security guards.

In the early years of Nazi rule, his mother, Paula, and father grew increasingly afraid of what their family's future in Germany would look like.

In 1938, with the Nazi's iron fist clenching around the country's Jewish population, the Kissingers made the decision to flee, first to London and then on to New York, where they arrived on September 5.

No answer.

See Jewish Library. How? Travelled abroad with the blessing of the German ministry of internal affairs and with the help of the precursursor to Mossad.

Also note that he is quoted as repeating the soap lie!