MAx peak to peak of ES without clipping?
The question is confusing, because while it asks explicitly about "clipping" distortion, the rest of the data seems to imply that the limit is a thermal one, which does not produce clipping per se.

But let's follow the reasoning regarding the thermal limit.

First of all, with a bias level of 0.01% of the peak current (this turns out to be about 1.4 mA), the amplifier is operating essentially pure "class B". The maximum theoretical efficiency of a class-B amplifier on a sinewave signal (when it is just barely clipping at the supply voltage) is &pi;/4, or 78.5%.

Each Darlington pair is limited to a temperature rise of 42&deg;C, using a heatsink that has a thermal resistance of 0.2 &deg;C/W, so that means we can have each pair dissipating 42 &deg;C / 0.2 &deg;C/W = 210 W.

This represents 21.5 % of the input power, which will then be 210 W/21.5% = 977 W, and since we have two pairs, the total input power will be 1954 W. The power delivered to the load will be 1954 W * 78.5% = 1533 W.

Since we know that the load resistance is 15&Omega;, we can calculate that the RMS current is \$\sqrt{1533 W / 15\Omega} = 10.1 A\$ and the RMS voltage is \$\sqrt{1533 W * 15\Omega} = 151 V\$.

Since the voltage gain of this amplifier is unity, the maximum continuous sinewave input signal is \$151 V_{RMS} * 2 * \sqrt{2} = 427 V_{P-P}\$.