The root problem is that mbrola/espeak has a serious bug with memory allocation. If you haven't checked for a new version, and reported the bug to them, that's the first thing you should do.
These warnings are emitted by glibc's malloc checker, which is described in the mallopt docs. If heap checking is enabled, every detected error with malloc (and free and related functions) will be printed out to stderr, but if it's disabled, nothing will be done. (Other possibilities are available as well, but that's not relevant here.)
According to the documentation, unless the program explicitly calls mallopt, either setting the environment variable MALLOC_CHECK_ to 0 or not setting it at all should mean no malloc debug output. However, most of the major distros (starting with Debian) have long shipped a glibc that's configured to default to 1 (meaning print the error message) instead of 0. You can still override this by explicitly setting MALLOC_CHECK_=0.
Also, the documentation implies that malloc errors go to stderr unless malloc_printerr is replaced. But again, many distros do replace it with an intentionally-harder-to-ignore function that logs to the current process's tty if pretend and stderr if not. This is why it shows up even if you pipe espeak's stderr to /dev/null, and your own program's as well.
So, to hide these errors, you can:
- Set the environment variable 
MALLOC_CHECK_ to 0 in espeak, which will disable the checks. 
- Prevent 
espeak from opening a tty, which means the checks will still happen, but the output will have nowhere to go. 
Using setsid, a tool that calls setsid at the start of the new process, is one way to do the latter. Whether that's a good idea or not depends on whether you want the process to lead its own process group. You really should read up on what that means and decide what you want, not choose between the options because typing setsid is shorter than typing MALLOC_CHECK_=0.
And again, you really should check for a new version first, and report this bug upstream if they haven't fixed it yet.