You can use molted feathers, however the amount of DNA on the tips of a molted feather is not as high as that of a freshly plucked feather, so it may be harder to extract enough DNA from a molted feather to find out. You can also use blood, and either have an avian vet draw some extra blood for you when doing a blood panel or snip a toe nail a tad too short. A broken blood feather would also great great!
Honestly, DNA sexing is good to know for health reasons alone. A male parrot can't lay an egg. Think about how many "male" parrots have been rushed to the vet for panting and having trouble pooping, then "plop" - there's an egg!
A few health issues can be ruled out by knowing the birds sex, since there are some sex-related problems that the other sex can't get, eggs being a big example.
About DNA Bird Sexing
-kicks self in the butt for having an 18 year old conure that has never been DNA sexed and has never laid an egg, but have heard of, and knows of, hens who didn't lay their first egg until 18+ years of age-