function A(){
    return new Promise(function(fulfill, reject){
        connection.query('SELECT * AS value FROM table_one', function(err, res){
            if(err){
                reject(err);
            }else{
                fulfill(res);
            }
        });
    });
}

function B(resultFromA){
    return new Promise(function(fulfill, reject){
        connection.query('SELECT * FROM something WHERE x = ' + resultFromA[0].value, function(err, res){
            if(err){
                reject(err);
            }else{
                fulfill(res);
            }
        });
    });
}

A().then(B, function(errorFromA){
    console.log("Error from A: " + errorFromA);
}).then(function(resultFromB){
    console.log("Result from A: " + resultFromB);
}, function(errorFromB){
    console.log("Error from B: " + errorFromB);
});