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.
No. Ug is not an allowable Scrabble word.
No. Najo is not an allowable Scrabble word.
No. Iv is not an allowable Scrabble word.
No. Ez is not an allowable Scrabble word.
Yes. Quale is an allowable Scrabble word.
No. Tir is not an allowable Scrabble word.
Yes. Ag is an allowable Scrabble word.
No. Wol is not an allowable Scrabble word.
Yes. Tech is an allowable Scrabble word.
No. Source: Collins Dictionary
Yes. Ho is an allowable Scrabble word.
Acronyms are not allowed in Scrabble, but nairu is an allowable Scrabble word.