A number of people, including myself, have tried to grow spinach in an AeroGarden.
Unanimous conclusion: Spinach doesn't like getting its toes wet. Normal spinach won't grow in an AG.
There are similar-to-spinach greens that will grow in an AG. I've grown swiss chard (it's not very well suited, but it does grow, ish), and tendergreen mustard (grows nicely, but needed liquid nutrients - yellowed on the salad bar series nutrients).
FWIW, if you have any outdoor container / ground space at all, and live in a temperate climate, swiss chard is much better outside, and ornamental. My outdoor chard have been growing strong May-November, and despite plenty of frosts, they're still quite happy, good to go another month perhaps, into New England winter. A most undemanding plant. If you have any lime, it adores alkaline soil.
But true spinach, not in an Aerogarden.