For past payments, you’d need to know what fee gets through at the time (it fluctuates quite a bit). Otherwise, no one can tell (a reason why Bitcoin keeps things anonymous)
What I often do is monitor the number of confirmations on the network on the blockchain. I spoke to a number of people, and they tend agree that the higher amount of the transaction, the more confirmations are needed before the transaction is accepted. Obviously, the more confirmations, the longer it takes.
I’m not saying there isn’t a problem with Gameflip, but they use Stripe (which uses Coinbase for BTC I believe), so it’s not like an unknown bitcoin provider.
I found this recent article (dated Jan 25, 2017) which describes how the BTC network slowed to a halt. With $0.55 miner fee, it still took 17 hours to confirm. It’s unfortunate as there’s so much promise in this currency.