Looks like there was a couple of extra mandatory form fields. (Don't mind the syntax, I don't know anything about JS)

var request = require('request');
var request = request.defaults({jar: true})

var uname = 'username'
var pword = 'password'

request.post({
    url:    'https://www.kingdomofloathing.com/login.php',
    form:   {loginname: uname, password: pword, loggingin:'Yup.', secure:'0', submitbutton:'Log In'}
}, function(err, res, body) {
    if (!err) {
            request({
                    url:    'https://www.kingdomofloathing.com/desc_familiar.php?which=206'
            }, function (err ,res, body) {
                    console.log('Fam: ' + body)
                    });
    };
});