The key to answering this question comes from application of raoult's law:
Partial Pressure of Liquid = (mole fraction of Liquid)(Vapor pressure of pure Liquid)
The liquid we're considering is water for both solutions. Therefore, the vapor pressure of pure liquid is the same. The mole fraction however is different. Mole fraction equals: Moles Water / Total Moles in Solution. (Note: Total moles = moles salt + moles water). The question tells you have 200g of water in both flasks, so the moles of water will be equal for both. The total moles however will be different because we are using different salts, each with different molecular weights.
The question asks, which flask will have the highest vapor pressure. The solution with the greatest mole fraction of water will result in the greatest vapor pressure. (Remember adding a nonvolatile solute decreases vapor pressure. The more salt you add, the more it decreases). To make the mole fraction greater, we need a salt that produces fewer moles per gram. This way, the denominator (total moles) would be a smaller number, which result in a larger mole ratio: (moles water / total moles).
Which salt produces fewer moles? Well, moles = grams salt / m.w. The salt that has a larger molecular weight produces fewer moles, so it's vapor pressure must be larger. In this case, (2g/74.5 (KCl) < 2g/58.4 (NaCl). Since there are fewer moles KCl, the mole fraction of water will be greater which explains why the vapor pressure is higher for KCl than NaCl (ie. it's closer to what it would be in a pure solution). You said this is false, but I think it's true... unless I made a mistake somewhere in my reasoning.
As for BP, volatility and BP are closely linked. A solution will boil when it's vapor pressure = atmospheric pressure. Decreasing the vapor pressure, will increase the boiling point. In terms of colligative properties, the boiling point elevation equals: (i)(kb)(m) where i = van't hoff factor (2 in this case), kb is a constant for the liquid (in this case for water), and m is the molality of the solution. The solution with the greater molality will result in a higher boiling point. The only difference between both KCl and NaCl is again, moles. molality = moles / kg solvent (kg solvent is the same). Therefore, the solution with greater moles salt will result in a greater molality. So NaCl, having more moles will result in a greater boiling point elevation. This makes sense because earlier we found that KCl will have the larger vapor pressure. NaCl on the hand, having a lower vapor pressure requires more heat to boil and so it will boil at a greater temperature (ie. it has a greater boiling point elevation).
