Since it's a KL codeshare flight I would say the KLM flying with partners website is your answer:
Ukraine International Airlines
- Business Class passengers can choose their seat from the moment they have booked.
- Priority check-in for Business Class passengers and for Flying Blue Elite and Elite Plus members.
- Checking in via KLM.com is possible if the Ukraine International Airlines (PS) flight (out- or inbound) is booked online via KLM.com. If not, please check in via the Ukraine International Airlines website or at the airport.
- You can access the Ukraine International Airlines lounges if you travel in Business Class, or if you are a Flying Blue Elite Plus member.
- Flying Blue members earn and spend Miles on Ukraine International Airlines flights with a PS or KL flight number.
Means you should have access to the lounge of UIA and priority check-in. As stated above by others just make sure to bring your physical FB Gold card.