Hi there. I noticed after duplicating and joining the fins together into a single object, the solidify modifier seems to be doing something weird to some of the fins. I'm not sure if there was a step I did incorrectly that's making it behave this way or whether the modifier isn't working correctly in my specific Blender version (v2.80.74), or what. I'm looking for advice if someone has seen this happen before!
One fin looks OK.
However, the fins on the other side of the object look like they're being folded in on themselves.
Here are the fins in wireframe top orthographic view.
Here are the modifier settings.
If I hide the modifier, each (flat) fin looks correctly positioned.
That's kinda goofy! Here's a workaround for you.
Before duplicating the fins around the rocket, click the "Apply" button in the solidify modifier. Then, you can duplicate the fins around the rocket and join them like normal. Do note that applying the modifier will make its effects permanent though, so make sure the one fin looks good before clicking apply!
I ended up solving the mystery! I had somehow inadvertently added duplicate vertices to my fins, which was probably confusing the solidify modifier.
I solved this by selecting all of the vertices of the fins and using the "Merge Vertices > By Distance" command. This removed the duplicate vertices and then the modifier results started looking correct again.