The Person A, B, C are employees of a company. If there are many, they should be on their on table with their own titles (one being Invoice Contact), linked to company. Then on the Invoice, I would put a field called Invoice Contact, that either auto enters or looks up the invoice contact person from the company/employee table. I don't think the button and yes/no is necessary, but the main question is, Is one person always designated the invoice contact person?. If so, in the employee table, on that employee's record is where I would put the check box--but don't think its needed.
If there is never more than one contact that is the Invoice/Billing contact for a given company, you can set up an additional relationship between a Tutorial: What are Table Occurrences?and company for that purpose:
Company::_fkBillingContactID = Contact|Billling::__pkContactID
Then you can refer to Contact|Billing on the invoices layout to show data about the billing contact
_fkBillingContactID can be set up with a conditional value list of just the contacts linked to that company in order to make it easy to select one as the billing contact.
Thank you both for the help. It's working for me now, and I can finally move forward past this roadblock.