Jabber is right in most of what he says with the exception of the "first pitch" part and the "never entered the game part." This is just confusion with the timing of the move.
Tom, with the way you have your line up written in the above example, it would have been handed back to us in MOST of our travel games (I say most because there were always some rare instances where umps occasionally did not fully understand the rule either, or just didn't care). If the flex is not playing defense in your scenario, then that is a "substitution," (i.e. DP is playing defense for the flex). This takes the game to 9 players. Therefore, as jabber mentioned, your lineup card should have reflected a defensive position for the flex. Then, AFTER the coin flip, the ump will ask if there are any changes to made to the line up. At that point you say, "yes, I want the DP to play defense in the game for the flex," and you are now at 9 players with your flex having only one re-entry.
While some have said this is "unconventional" we often used this tactic, and one of the Bandits teams we frequently faced (Tyrrell) did it EVERY game we played against her regardless. Remember, the rule states you cannot go to 10 starters (i.e. use flex/DP) once the game has started. Therefore, if you list a flex to start and "sub in" the DP on defense (for the flex) after the coin flip you are essentially starting the game with 9 as you normally would and allowing the possibility that you MAY go to 10 players IF YOU CHOOSE at a later point in the game by bringing in the flex. Many people who have to manage large rosters will use this move, especially in some of the elite circuits because it gives you more flexibility with your substitutions. Let's say you have a pitcher that is a complete stud and you need her to shut down the other team so you can get an early lead and then save her arm. However, at NO POINT in the game do you want to lose her bat. With the DP flex rule, you could bring in another pitcher (who you listed as flex) to throw in the later innings, while still keeping the stud in the lineup to hit, or even hit and play SS if you need... your choice. You also could just bring in another straight sub for her (while still keeping the option of bring in a flex open) if you choose. Again, because of the flexibility it gives you, if you really know ahead of time how you want to use the talents of EACH player on your team to maximize your chances of winning and getting more people in to play (in one capacity or another) it makes sense to use a DP/Flex. It was always amazing to me though how some teams would look at you cross-eyed when you subbed out the flex after the coin flip?!