DP Flex rule???

[slowballbaker]

Need help with this one...

A team starts with the DP/Flex. At the start of the game the coach tells the umpires that the DP will enter the game to pitch.

The DP then bats and gets on base, so the Flex enters the game and runs for the DP. Would this be considered a courtesy runner or a substitution or neither...

The next half inning the DP re-enters for the flex and pitches continues to pitch.

Then the next time the DP bats she gets on base again, then the Flex enters the game and runs for the DP again...

Questions: Is the DP/Flex under the same one re-enty rule???
Would the DP be a dead player at this time??
Or would this be considered a courtesy for the pitcher?

Thanks