If so, how much? Can that money be held in escrow by a third party?
Are you willing to go to jail for your customers? For how long?
If a customer orders 134 phones ($10k), will you comply with any relevant federal financial disclosure guidelines?
If served a national security letter that includes a gag order, how will you react?
Will you accept cash transactions through the USPS, with only $75 and an address enclosed?
Can you prove that records are not kept? How?
These questions are partially rhetorical, but for people who want/need anonymity, they're important.
edit, to keep questions in one spot:
How do you anonymize shipping? It's straightforward to find ways to accept anonymous payment, but how do you keep the Man from following all outbound packages from burnerphone?
What are advantages over buying a gift card with cash and purchasing a phone online or through an intermediary?