Golduck can only be found in Safari Zone (Area 3) Via Surf.
It has only 5% Encounter Rate but if we use the Repel Trick with a Lv. 31 Pokemon it goes up to 48.72%.
In addition if we have a Pokemon with the ability Illuminate, Arena Trap or No Guard the wild Pokemon encounter rate is doubled.
Golduck has 16.78% Catch Rate.
NOTE: I did’t use the Repel Trick with a Lv. 36 Pokemon to only encounter Golduck because this way his Encounter Rate is extremely low.