The wonder multistorey garden (WMSG) is an innovative vertical farming system tailored for urban settings that can be constrained by the irrigation regime, and by types and levels of fertilizer application. This study evaluated the effects of applying NPK fertilizer and black soldier fly frass fertilizer (BSFFF) under different irrigation regimes on the growth, yield, and pest infestation of kale (Brassica oleracea) and Swiss chard (Beta vulgaris). The fertilizers were applied at rates equivalent to 371 kg N ha−1. For each crop, the BSFFF or NPK was applied to supply 100% of the N required (100% BSFFF), and then a combination of BSFFF and NPK was applied so that each fertilizer supplied 50% of the N required (50% BSFFF + 50% NPK). Crops’ water requirements were provided using three irrigation regimes: daily, every two days, and every three days. The control treatment was not amended with any fertilizer, while water was provided ad libitum. The results revealed that the irrigation regime significantly affected the leaf production of both vegetables. Irrigation regimes significantly influenced kale plant height, where plants provided with water daily achieved the highest average heights of 20 cm, 46 cm, and 54 cm at 14, 28, and 42 days after transplanting (DAT), respectively. Furthermore, the application of 100% BSFFF produced kale with significantly higher plant heights (55 cm) and number of leaves (9.9 leaves) at 42 DAT compared to other treatments. The interaction between irrigation regimes and fertilizer significantly influenced kale height at 14 DAT and 42 DAT. Use of daily irrigation regime and 100% BSFFF produced the tallest kale plants of 59 cm at 42 DAT. Application of 50% BSFFF + 50% NPK or 100% BSFFF with daily irrigation achieved the highest values of kale and Swiss chard leaf chlorophyll concentration, recorded at 42 DAT. Fertilizer application significantly affected pest population, with the lowest pest infestation being recorded from kale and Swiss chard grown in soil amended with BSFFF. The application of 100% BSFFF or NPK, together with daily irrigation, significantly increased the fresh shoot weight and leaf dry matter of kale and Swiss chard, as compared with the control. The fresh shoot yields of kale and Swiss chard achieved through using a combination of 100% BSFFF and daily irrigation were 14–69% and 13–56% higher than those of NPK, respectively. The same treatment combination also produced kales and Swiss chard with 8–73% and 16–81% higher leaf dry matter compared to NPK, respectively. It was noted that soil amendment with BSFFF maintained higher values of kale (41–50%) and Swiss chard (33–49%) leaf dry matter compared with NPK treatments, during periods of water stress. Our study has demonstrated the high potential of single (100% BSFFF) or combined applications of BSFFF (50% BSFFF + 50% NPK) with a daily irrigation regime to improve the growth, yield, and pest management in Swiss chard and kale under vertical farming. Our study advocates for the scaling of WMSG and BSFFF for sustainable food systems in urban settings.