At the time of writing the original post, I was unable to retrieve all berry species of the identified flowering plant orders within a reasonable time. After all, I am not sure why this happened. However, it is important that the implicit EntityClass functionality works, so I tried again today and with susccess. So this is an addendum to the post above: the code to retrieve all common names available for berry plant species associated with the "flowering plant" orders is:
BerryCommonNames =
EntityValue[
EntityClass[
Flatten@EntityValue[order,
EntityProperty["TaxonomicSpecies", "SpeciesList"]], All],
"CommonName", "Dataset"] // DeleteMissing
