StarryCamera is the best camera app for a starry sky.

-----
# How to use
1. Mount your iphone on a tripod.
2. Choose shooting mode.
3. Choose ISO, Shutter Speed.
4. (Choose White Balance according to your preference)
5. Tap the shutter button.

# About 5 modes
Starry sky mode : Highlight bright stars, and increase contrast.
Star trails mode : Lighten blend mode for star trails.
Milky way mode : Increase contrast.
Night view mode : No image processing.
Lighten mode : Lighten blend mode. (for firefly, light trail, etc)

###
If the app crash often on old iPhone, try to choose small resolution in the preferences view.