How to measure saturated salinity and mineral levels for flaked sea salt?
Why not use salt (NaCl) bought from a store, or even better at a defined purity grade from a chemical vendor?

When you use sea salt, you get lots of other ions but more importantly you get colloidal particles, organic substances, and other compounds that will affect the crystallization. Chunky results sounds to me like a colloid particle that started crystallization in all directions at once.

If you want perfect crystals, do it perfectly, i.e. with a pure solution, in a clean and new glassware or polished stainless container. If you want perfect crystals you have to reduce the new-age-ness of it ;)

As for understanding, nobody fully understands crystallization, but a lot of things are known. There are books on this topic, check amazon and search for "crystallization". As for instruments, x-ray fluoroscopy and diffraction wouldn't be amiss but you will get very far with an optical microscope, I know I can watch crystals through a microscope for hours and still find something interesting. Barring XRF, XRD and microscope, and within a household budget there are salinity measurement probes and conductance measurement probes which will be able to tell you something of the brine such as it is.