The insect in the photo is the spinach flea beetle, Disonycha xanthomelas. This is not a well researched species of flea beetle. A few of the other plants I can find reference to it feeding on are beets, Swiss chard, lamb’s quarters, and chickweed. One reference I have states that on rare occasions they are known to damage cabbage, horseradish, lettuce and radish.
Both adults and larvae feed on leaves, which is interesting because larvae of most of our common flea beetles feed on roots.
The “Handbook of Vegetable Pests” states that “generally, these flea beetles are not considered serious pests”.
Foliar insecticides can be effective, but if you are leaning towards not using insecticides row covers may be an option to prevent feeding, if that is practical.
Let's just hope they don't find the spinach I have growing in the garden space around my house. So far, it looks very nice.
Thanks John, for sharing your knowledge with us gardeners.