1.可以 fly a small plane 或 take a small plane 但不能 fly in a small plane
2.用in,on 时,一般用on.但有些具体情况下也可以用in.比如可以 sit in a small plane ,how many people are there in （on 也可以） this plane?
3.当 fly a plane 的时候 如果再说 in the sky 在考试中就属于病句（累赘）.
4.an airport nearby 改成 a nearby airport 读来比较顺口.
所以可以说成：one day we took a small plane from a nearby airport.