The main issue wasn't the fact that she could get out (because I often use an uncovered chicken wire surround as a temporary "pen" when transitioning from brooder to run access) - the main problem was she couldn't get back in. This is why chick door/panic door openings are recommended, so chicks can come out when they feel safe but retreat back into a safe zone when pursued.
Assuming you go with the same set up as current, either 1) securely cover the top of the pen so no more fly outs or 2) raise the entire pen so chicks can get IN and out.
For example, this is my temporary chicken wire set up for transitioning the chicks to using chick doors set up in front of the brooder itself. Notice the bricks around the bottom? I can place the wire on top of the brick to create gaps around the entire base that are big enough for the chicks to escape through, but the adults won't fit. (As your chicks are older than the 2-week-olds here they'd likely need a bigger opening than 1 brick high, but this is just an example.)
You also didn't include any photos of your set up. Do you have ample space AND clutter to provide hiding places for chicks when they're out and about? Multiple feeders spread out, to reduce risk of aggressive action around food bowls? I integrate very early (I start letting them interact face to face with adults around 10-14 days old), but it does require some setting up to do so safely.
Assuming you go with the same set up as current, either 1) securely cover the top of the pen so no more fly outs or 2) raise the entire pen so chicks can get IN and out.
For example, this is my temporary chicken wire set up for transitioning the chicks to using chick doors set up in front of the brooder itself. Notice the bricks around the bottom? I can place the wire on top of the brick to create gaps around the entire base that are big enough for the chicks to escape through, but the adults won't fit. (As your chicks are older than the 2-week-olds here they'd likely need a bigger opening than 1 brick high, but this is just an example.)
You also didn't include any photos of your set up. Do you have ample space AND clutter to provide hiding places for chicks when they're out and about? Multiple feeders spread out, to reduce risk of aggressive action around food bowls? I integrate very early (I start letting them interact face to face with adults around 10-14 days old), but it does require some setting up to do so safely.