Yes, if the RKV can deliver 3 watts/channel into a headphone impedance of 100 or more ohms, by all means they should be able to drive the K1000s. I was assuming that the RKV amplifier was one of those flea-powered 1-3 watt/channel at 8 ohm SET type amps that are popular with some audiophiles.
With the K1000s, even at a more than reasonably loud listening level, you are probably only using an average of 1/10th watt of power, with peak power levels approaching 1 watt or slightly higher. Even if you could tolerate peak levels much greater than 1 watt, it is unlikely that these momentary high power levels would damage the K1000s, but perhaps not so for your ears.
Assuming the Fisher 400 can provide 28 watts/channel into either 4/8/16 ohms, off of the 4 ohm transformer tap we were using, the available power into 120 ohms was not more than 0.9 watt/channel into 120 ohms. Theoretically, the available power off of the 16 ohm tap would have been 3.5 watts/ channel into 120 ohms, but I did not try this to see if it sounded any better or worse than the 4 ohm tap I normally use.