One important note—it should be ground flaxseed because if you eat the seeds whole they will generally pass through your gut completely intact.
I’m no expert but I think you’d definitely want some omega-6 fatty acids in the mix, probably a minimum of 50:50 omega-6:omega-3. Both are “essential” fatty acids, meaning that they are required by the body.
I think that a person can thrive on a low-fat diet, but I don’t know what the advisable lower-limit is.
Personally, I’m experimenting with a WFPB diet where I eat very little or no added oil in dishes I prepare for myself. I usually eat a tablespoon or two of nuts every day (mostly walnuts, which have the largest proportion of Omega-3 ALA of commonly available nuts) and every few days I’ll eat at local vegetarian places that do veggie bowls which always include a mix of different fats. I’m currently taking about 1500 mg/day of algae-derived omega-3 supplements which contain EPA & DHA. About once a month I eat fish because I enjoy it, but aside from that, the quantity of animal-derived foods I eat is pretty minimal.
One time, a guy ate a nearly fat-free diet for about 6 months. The goal was to induce and observe the expected deficiency syndrome. Instead, that did not happen, but it permanently cured his migraines and he no longer felt tired after a day of work.