How to do this is described in Section 8.1.1 of the manual (memman) for memoir by setting \parindent to 0em. This can be done by, for example, perhaps,
\setlength{\parindent}{0em}
The manual also suggests setting \parskip to a positive length to give some vertical space between paragraphs. However, consider what happens when a non-indented paragraph ends at a page break and the last line is full. The following non-indented paragraph will start at the top of the next page; the reader will assume that the two paragraphs are actually just one. In general, typographers dislike this style of paragraphing except when they can have manual control of the layout of each page.