No, you do not need to provide UPC or ISRC codes to DistroKid.
DistroKid has been appointed by the US ISRC Agency to assign ISRCs, and will automatically generate new DistroKid ISRC codes for every song you upload. It's free and automatic.
You can specify your own ISRC codes if you have a Musician Plus or Ultimate account.
More info on providing your own ISRCs to DistroKid.
If you want to apply for a UPC issued by GS1, please contact your local GS1 office here.