Well I have no idea what the tournament rules stated exactly, but the flex position is not a batting position. The flex batting should be an illegal substitution and disqualification of that player.
You can't add players (to the lineup) after the official lineup has been accepted by the umpire. You can't go from 9 to 10 after you have officially entered the lineup (given it to the umpire).
With the DP/Flex you can go forwards and backwards but that isn't what we are talking about here.
She didn't hit for anyone. She was in the lineup as the 5 hitter, just not on the card. They had 10 players and batted all 10. We caught it her 1st time at bat, but thought they had just put the wrong # on the card. The result of that AB was insignificant, so we let it go. Next time through, we realized what happened. He forgot to put this player in his lineup. Ironically, it was his own daughter.
An eligible team member may be added to the lineup at any time, even after it has been submitted to the umpire. There is a warning that goes along with it in NFHS, but other than that it is nothing. No, the dp/flex may not be used after the lineup card has already been submitted, it must be made known at the start of the game.
I'm confused based on this post and the OP...
You stated in the OP that this was the Championship game, but no mention of any tournament rules allowing extra batters. You did say free substitution in pool play, but that does not necessarily mean "bat everybody"
Under the NFHS rules, the most batters you can have in the lineup is 9. The DP/FLEX option allows a 10th player on the lineup list, but you still only have 9 players actually batting.
Two questions:
1. How many batters were listed on this team's lineup?
2. Was #13's correct name name listed in the lineup, but with an incorrect number?
If the team had a total of 10 players, but only listed 9 in the batting order, all you have here is an unreported substitution when the number five batting position came up.
You said that #13 was batting in the fifth spot in the order, but she was not on the card. Since SOMEBODY had to be listed on the lineup as the #5 hitter, then when #13 hit in that spot she was an unreported substitute.
When discovered, this is what should have happened:
#13 is added to the lineup card as an available substitute
#13 is now in the game as the batter in the 5 hole
Whoever was batting in the 5 hole has left the game and has a re-entry available
Team warning for adding #13 to the lineup
Team warning for the unreported substitution of #13 into the game
Play ball
If the team listed 10 batters and a tournament rule allowed this, it brings up some more questions which can be asked if needed.
An eligible team member may be added to the lineup at any time, even after it has been submitted to the umpire. There is a warning that goes along with it in NFHS, but other than that it is nothing. No, the dp/flex may not be used after the lineup card has already been submitted, it must be made known at the start of the game.
Tournament rules when bracket play starts is straight 9 with subs, or 10 with a DP/Flex. Normal NFHS rules. #13's name and number were not on the card. He forgot to put her on the card, and admitted so. She had 1 AB in the 5 hole which alerted us to the problem, but the AB was an out, so it didn't affect anything. When we figured out what had happened, (after her 2nd AB which was a double that drove in a run), we reported to the umpire before the next pitch had been thrown.
Answer to your questions:
1. 9 position players on their lineup
2. #13's name nor number were on the card anywhere.