Answer:
I presume that your opponent ultimately built the word FLAX off of the A in AVOW. If your opponent did this in one turn he would receive the appropriate points for FLAX since that is a legal word.
If your opponent laid the X and claimed AX, his turn is over. If you follow the rules scrupulously, saying he is done then laying the FL would be going out of turn.
Unless you are in tournament play, following the rules that closely usually causes people to avoid playing with you.