Is the iPhone magnetometer sensitive enough to detect solar storms?
I don't think anyone here will be able to give you a definitive answer to this, unless of course they've tried to do something similar.

Apple only provides very basic specs in terms of its sensors (e.g. accelerometer, gyro, proximity, compass, barometer, etc) and doesn't go into their individual specifications.

However, considering that anyone can build a magnetometer from easily available materials to measure slight changes in Earth’s magnetic field due to solar storms, my guess would be that an iPhone's magnetometer will pick up on these fluctuations as well. But of course, this is nothing more than an educated guess.