My Zambian Tonga instructor (another Bantu language with similar consonant duos we don't see in English) suggested saying another word that ends with the first letter and then the root, practicing that awhile, and then dropping the beginning of the first word. For example: mzuri, say something like "mom zuri," blend it together "momzuri" and then drop the "mo." It takes some practice, but I found it helpful. Also, there are lots of places to listen to Swahili by native speakers. I particularly like Sauti Sol songs (found in all the usual music places), and Ubongo Kids tv episodes, which are available on YouTube.