I'm trying to design a linear power supply to provide 32V and up to 10 amps from a 50V source. Is this the correct way of using multiple LM338 regulators to achieve this?
The LM338 has an input-output voltage differential of 40V, and you've got those great big caps in the feedback path. That will cause the output to start low and ramp up slowly (8-10 volts/second) -- so unless that 50V supply ramps up slower than that, you have problems. You can alleviate this with zeners across the in/out pins, though.
The LM338 has 50 to 100\$\mu\$A of current coming out of its adjustment pin. That means that the output voltage, as you've designed it, is between 36V and 41V. You need to reduce the values of all the resistors so the standing current in the adjust resistors better swamps the current from the adjust pin.
They're not going to share current nicely. One will try to carry the whole load until it fries, and then the other will try until it fries. Generally you want to design one power supply; when things get this power-hungry, you want to use a controller chip (like the LM723, if you insist on being old school) and pass transistors.
They're going to get hot. You're dropping 18V at 5A -- that's 90 watts per device. The junction-to-case thermal resistance is 0.7 degrees/W, so you would need to keep the case at 62 degrees C to keep the junction temperature to 125 degrees C. That's going to limit the ambient temperature you can operate in, and even assuming a 25 degree C room temperature (which, trust me, is unrealistic), you'll need a big heat sink.