Recently, I answered a similar type of question. The reasoning for that question is also applicable for this answer also.
Electrostatic force between potassium cation and chloride ion is way stronger than that with nitrate ion. So, more energy is needed to break the bond between potassium chloride than potassium nitrate. Hence, lattice enthalpy is more in case of potassium chloride and thus more water is needed to dissociate the bonds. So, potassium chloride is less soluble in water.
You can compare the solubilities of potassium nitrate and potassium chloride by observing the graph taken from this site:
You can observe that solubility of both potassium chloride and potassium nitrate is same at approximately 23℃ but then as temperature is increased, solubility of potassium chloride increases steadily but solubility of potassium nitrate increases drastically.
So solubility order:
Potassium nitrate > potassium chloride