Let's write the reaction first:
2 Au + 2 BrF₃ + 2 KF → 2 KAuF₄ + Br₂
To know which of the substances is the oxidizing agent, calculate the oxidation numbers of each element before and after the reaction. If the element's oxidation number decreases, then that is the oxidation agent. Let's calculate Br.
BrF₃: x + 3(-1) = 0; x = +3
Br₂: 0 (for any elemental form, oxidation number is 0)
The oxidation number is reduced from +3 to 0. Thus, BrF₃ is the oxidizing agent.
