The trophy unlocks when Kenny appears in lieu of Monica at the successful completion of a mission. Normally, his appearance is random and quite rare. However, you can change the low possibility of his showing up into a probability. Note that if you have unlocked the Come Back, Kenny! trophy in the DLC, the save transfer will not credit you with this achievement. In other words, Kenny must serve you in the standalone game for this trophy to unlock.
Play with a party of four human players. Accept any mission from Monica that you know you can complete without dying. Do not pick up any food at the camp. Similarly, do not pick up any food on the battlefield. Upon successful completion of the mission, Kenny will appear.
One option is to play the Daily: Infernal Invaders with four human players. You will not have the choice to take food with you on the mission. There is no food available to be picked up during the mission. At the end of a successful completion, Kenny will appear and unlock the trophy if not already earned. Even if you have only three players, when you press quick play for the daily mission, it is quite likely a fourth human player will join. If so, Kenny will appear once the mission is successfully completed.
Kenny is most likely to appear when four players, human and AI, survive the mission with empty food 'baskets.' I say 'most likely' because I do not know if this is 100% effective. Nevertheless, Kenny has never failed to appear for me when all four players, human and AI (if present), finish the mission with empty food 'baskets.'