You can get from there the transaction size, and multiply yourself with the amount/vByte you want to pay.
Given that he is transferring coins from an exchange's cold storage to the exchange's trading wallet, then it will (presumably) be a simple 1-input-2-outputs. It can't be part of a batch transaction if they are letting him pick a custom fee, or at most, a very small batch transaction with only a small handful of other users who have picked a similar fee in the last few minutes. A quick look on the BitOasis website however seems to suggest that their cold storage might be multi-sig, in which case transactions will be significantly larger and more expensive.
The fact that they don't tell you how big the transaction will be, and they also don't make it clear if you are calculating sats/byte or sats/vbyte is a pretty big oversight in my opinion. Best case scenario, 1-input-2-outputs could be around 180 bytes. Worst case scenario with a large multi-sig you could be 1000 bytes or more. Picking a large fee of 100 sats/byte could end up costing you more than 10% of your coins.
Perhaps it will tell you on the next page what the total fee will be? If you are in a hurry you will need to pick 90-100 as NeuroticFish has said an accept you could end up paying a very large fee. If it were me, I would pay a tenth of that and just wait for a few days.
Can you tell us what exactly exchange you are talking about(the exchange where you want to make a transaction to send to their trading wallet)?
It says BitOasis in the picture he linked.