Redirection of standard output is a very simple trick that's been around pretty much forever. The exact mechanism for it varies from platform to platform, but once you know how to do it, it's pretty easy.

Simple solution:
Redirect STDOUT to a file. Run compiler. When compiler is finished, read the text file to the memo component. You get all your output all at once.

More complicated solution:
Redirect STDOUT to a file. Run compiler. Continually check the file to see if it contains text. If it does, place this text into the memo component and clear the file.

There's probably even a way to redirect STDOUT to some sort of memory stream instead of to a file. Not certain, though.