Is there a Successor or an Alternative to mk-parallel-dump?
A bit late to the party but as a former mk-parallel-dump user I came across the same question recently.  I tried using the parallelism feature of MySQL mysqlimport however that only works for different tables even if you break up the dump files into smaller chunks.  Shame.

However I then discovered MySQL Data Dumper which is apparently being developed/maintained by Percona people.  

MySQL Data Dumper project page

There are source tar balls for the various versions downloadable here:

Source downloads

The latest release supports dumping of AWS RDS instances too.  A typical invocation might be like:

./mydumper --user=root -o dump --rows=100000 -B database_name
./myloader --user=root -d dump -B database_name


You can also chunk by statement size, or number of output bytes.  By default dumping and loading use four threads, but you can set this.  There are a number of options available to control locking strategies and limiting which tables are dumped (the examples above do all the tables). For dumping across a slower network connection it supports data compression. 

So far my experiments have been good although as ever I think you have to be careful to optimize MySQL for heavy parallel write access to get the best import time paying special attention to things like InnoDb log file and buffer sizes and concurrency settings.