It is not an easy question to answer. I believe you are confused because you don't see any reason not to use "independently" in place of "independent". In order to understand the sentence, you need to separate each part as follows:
a firearm owner (subject) possessing such a mould (present participle clause
modifying the subject) can obtain (modal + transitive verb) a supply of those
bullets (direct object) independent of unreliable manufacturers and
distributors (adjective modifier or dangling participle).
"independent of..." is an adjective phrase (dangling modifier) that modifies the subject. Some grammarians explained that the present participle being is omitted as follows.
a firearm owner possessing such a mould can obtain a supply of those
bullets being independent of unreliable manufacturers and distributors.
"Being independent..." is a dangling participle which modifies the subject's state.
Regardless of whether you consider "being" is omitted or not, the most important function of "independent" is to modify the subject and it should be in the form of an adjective in order to do it (Example sentence in the link: Tall and slim, she’s an exceptionally striking woman).
If you split the part into two sentences, it will be more clear and easy to understand.
(1) a firearm owner possessing such a mould can obtain a supply of those
(2) a firearm owner is independent of unreliable manufacturers and distributors (when obtaining a supply of those bullets).
You can visit the above link to understand more about "adjective modifier" or "dangling participle".