As an artist I am often asked where I get my materials and what materials that I use. So for anyone new to Dubai or wondering where you can get art supplies from then the main shops I go to are Kazim at 'Magrudy's Mall' on Beach Road (near the flag past Mercato towards Diyafa Street) It is at the other end of the mall to Magrudy's on the ground floor and is a stationary shop but sells a lot of artists materials including canvases, oil paint, acrylic paint, artists papers, brushes etc. In fact almost anything you might want!
The other place I get my materials is Emirates Trading. They have a big branch near Maktoum Bridge and also smaller branches at DIAC, DUCTAC and Bin Sougat Centre amongst others. The nearest one to 'New Dubai' would be in the art centre at Mall of the Emirates, on the 2nd floor, access from the car park.