Do flutes improve with age like violins?
In short, no. The long answer is a 30 year old student flute will only play as good as it’s mechanics will allow, and at 30 years old it would be showing wear & fatigue and a newer student flute will play circles around it. In addition there have been many improvements in head joint and embouchure hole design so a newer flute has advantages here as well. In the case of expensive hand made flutes, they may or may not play as good as their modern counter parts but they will not “improve” just due to their age. In fact the modern scales and higher pitch of the newer flutes make it a better choice in most cases.