Luke 2:39

And when they had accomplished all things that were according to the law of the Lord, they returned into Galilee, to their own city Nazareth.

Luke omitted the flight to Egypt and other important details of the life of Christ at this point, making it exceedingly unlikely that he had a copy of Matthew available to him. Even if he had, such omissions are characteristic of Luke's style. Another example was cited by Childers:

The same sort of writing occurs in Acts 9:25,26, where it appears that Paul returned to Jerusalem shortly after his conversion; but in Galatians 1:17,18, we learn that three years elapsed before his return. Such omissions are common in Scripture and other ancient writings.[32]