Flint billing is what you owe Flint and any account credit you hold against it: per-event fees, Flint's subscription charges to you, corrections to fees already charged, credit Flint issues you, and the collections Flint takes out of your Flint balance. It is separate from subscriptions, which is you charging your own customers.
A merchant billing balance is one currency's current position: outstanding_money is what you owe now, available_credit_money is credit you hold and have not used, and observed_at is when the snapshot was taken. Both amounts are unsigned, and credit reduces what you owe only when Flint applies it. merchant_billing_balance_id is stable per currency, so you can fetch the same balance again by ID.
A merchant subscription invoice is an invoice Flint issued to you. subtotal_money is the amount before credit, credit_money is the credit applied to it, total_money is subtotal minus credit, and outstanding_money is what is left to collect. Lines are subscription or credit.
Flint collects what you owe out of your Flint balance, which posts a merchant_billing_payment balance transaction with a negative amount and no fee. A reversed collection posts a merchant_billing_payment_reversal with a positive amount, whose related_balance_transaction_ids holds the ID of the collection it reverses. Both appear on money movement, and a collection made against a Flint invoice can be found with GET /v1/balance-transactions?related_object_type=merchant_subscription_invoice.
These routes are read-only and need the merchant_billing.read scope. For entry-by-entry history, generate the merchant_billing_itemized_v1 report. See Flint Billing for the eight entry types and their signed effects.