The ToS state: "If you wish to terminate your account, you may do so by following the instructions on the Site or through the Services".
However, there seem to be no instructions anywhere, let alone a deletion link. Perhaps try to request deletion at the address named under Contact Us: firstname.lastname@example.org.
Publicly visible text/images often aren't properly deleted even when you succeed in deleting an account. Try editing or deleting them manually before deleting the account itself. If you're unsure what happens to your tracks you can always contact QuickMeme and ask personally. By the way, deletion requests don't necessarily mean your data will actually be deleted (e.g. due to legal obligations).
If you signed up for QuickMeme using a third-party login such as Facebook or Twitter, you probably want to revoke all access from QuickMeme. Click the icon below to find out how.