Temporal lobe aneurysm

At various points in the documented life of Dumbo he begins to hear others singing rather than speaking to him. Although that could be a purely escapist fantasy to avoid confronting his own mundane dilemmas, it would be remiss to not think about the possibility of these being auditory hallucinations (defined as sensory stimuli in the absence of external sensory stimuli). These events are rare, but documented, resulting in all voices being heard as song - or maybe for Dumbo it's as simple as hearing crows "singing" songs about you. A CT should be requested as a matter of course although it would be a challenge to accommodate him into a scanner.
Fragile X Syndrome

The picture I get of Dumbo's life is one of psychogenic muteness, repetitive behaviour (the same jump into the bucket of pie filling ever night), social anxiety, peer teasing and difficulty with physical feats - most recently the elephant pyramid disaster -resulting from poor muscle tone. This, coupled with his appearance, suggests the possibility of Fragile X syndrome - a genetic disorder caused by mutation of the FMR1 gene on the X chromosome predominantly in males. It would also explain why Dumbo's mother was so secretive about his birth using a stork delivery service rather than a hospital to avoid questions which may have been raised regarding her family history.

Vertigo

 A belief that you can fly is more often than not, incorrect. Even given his enlarged ears, it is near impossible that Dumbo can lift his own body weight off the ground. Add to this the physiological impracticality of "flapping" ones ears and the result is that we must assume that Dumbo cannot actually fly. We are therefore left with an assumption that Dumbo experiences what could be misinterpreted as "flight" - the sensation of swaying while the body is actually stationary with respect to the surroundings. Inner ear problems are often the cause of vertigo as the act to effect the balance mechanisms of the vestibular system. Given Dumbo's aforementioned distended auricular protuberance


Schizophrenia

All of these symptoms could be brought together in a single diagnosis: schizophrenia. Dumbo reports adiutory hallucinations, visual hallucinations and delusional beliefs about flying and his famed destiny. There is a suggested family history of odd behaviour: when Dumbo's mother assaulted those teasing Dumbo, she is judged to be "mad" by the other circus performers (and locked away). There is a strong genetic component to schizophrenia making the diagnosis more likely. A trial of antipsychotics may be in order - I would suggest Seroquelephant.