It was in 2006 (1) / that we first flew (2) / to the United States. (3) / No error. (4)

Answer

2

Explanation

when will replace that because – when is used in time clauses to say that something happened, happens, or will happen at a particular time.
Look at the examples given below:
He left school when he was sixteen. The last time when I went to Scotland, the weather was beautiful. Hence, when we first flew is the right usage.