The CFLC does not apply to non-FFL dealers.
A private party does not need to obtain a verification number prior to shipping a firearm to a CA FFL dealer.
CA DOJ BOF says...
I am not an FFL but I want to ship a firearm to a California FFL. Do I have to obtain a Firearms Shipment Approval number before shipping a firearm to California?
No. The requirement to obtain a Firearms Shipment Approval number only applies to holders of valid FFLs.
Penal Code 12072
(f)(1) (A) Commencing July 1, 2008, a person who is licensed pursuant to Chapter 44 (commencing with Section 921) of Title 18 of the United States Code may not deliver, sell, or transfer a firearm to a person in California who is licensed pursuant to Chapter 44 (commencing with Section 921) of Title 18 of the United States Code unless, prior to delivery, the person intending to deliver, sell, or transfer the firearm obtains a verification number via the Internet for the intended delivery, sale, or transfer, from the department. If Internet service is unavailable to either the department of the licensee due to a technical or other malfunction, or a federal firearms licensee who is located outside California does not possess a computer or have Internet access, alternate means of communication, including facsimile or telephone, shall be made available for a licensee to obtain a verification number in order to comply with this section. This subdivision shall not apply to the delivery, sale, or transfer of a short-barreled rifle, or short-barreled shotgun, as defined in Section 12020, or to a machinegun as defined in Section 12200, or to an assault weapon as defined in Sections 12276, 12276.1, and 12276.5.
(B) For every identification number request received pursuant to this section, the department shall determine whether the intended recipient is on the centralized list of firearms dealers pursuant to this section, or the centralized list of exempted federal firearms licensees pursuant to subdivision (a) of Section 12083, or the centralized list of firearms manufacturers pursuant to subdivision (f) of Section 12086.
(C) If the department finds that the intended recipient is on one of these lists, the department shall issue to the inquiring party, a unique identification number for the intended delivery, sale, or transfer. In addition to the unique verification number, the department may provide to the inquiring party information necessary for determining the eligibility of the intended recipient to receive the firearm.
The person intending to deliver, sell, or transfer the firearm shall provide the unique verification number to the recipient along with the firearms upon delivery, in a manner to be determined by the department.
(D) If the department finds that the intended recipient is not on one of these lists, the department shall notify the inquiring party that the intended recipient is ineligible to receive the firearm.
(E) The department shall prescribe the manner in which the verification numbers may be requested via the Internet, or by alternate means of communication, such as by facsimile or telephone, including all required enrollment information and procedures.