What can cause these flattened nails?

This nail dystrophy presents with laterally inverted and centrally depressed nail plates. It is tested with the 'water drop test' or 'bead test'. If the water drop or bead stays in place, balanced on the nail it is a positive test for koilonychia, which translates from the Greek for hollow nails, or 'spoon nails'. It may be a sign of serious underlying health concerns.

Koilonychia can be associated with chronic iron deficiency, lichen planus, psoriasis, hyper/hypothyroidism, onychomycosis and a myriad of other autoimmune, vascular or musculoskeletal disorders. It is a sign present in 37–50% of patients with Plummer-Vinson syndrome, characterised by iron deficiency anemia, dysphagia and esophageal webs. Spoon nails have been noted to be present in around 49% of those with hemochromatosis. 

Koilonychia presenting with iron deficiency anemia should prompt investigations for malnutrition, GI blood loss, or malignancy. Noticing spoon nails on a patient may also prompt the clinician to perform a skin check for signs of psoriasis, lichen planus, or twenty-nail dystrophy.

In this man's case, hemoglobin, iron studies, thyroid function tests were all carried out, and returned normal. 

Iron deficiency anemia, inflammatory skin disease, and fungal nail infection are the most commonly implicated causes that are reversible. 

In the example of chronic iron deficiency, nail spooning is usually reversible with iron supplementation and nutritional improvement, as well as fixing the source of blood loss from underlying malignancy, GI ulceration, etc.

In some cases, as in this man, koilonychia can be hereditary or congenital and does not have a target for reversal.