Viscoelastic microfluidics leverages the unique properties of non-Newtonian fluids to manipulate and separate micro- or submicron particles. Channel geometry and dimension are crucial for device performance. Traditional rigid microfluidic devices require numerous iterations of fabrication and testing to optimize these parameters, which is time-consuming and costly. In this work, we developed a flexible microfluidic device using ultra-stretchable and biocompatible Flexdym material to overcome this issue. Our device allows for simultaneous modification of channel dimensions by external stretching. We fabricated a stretchable device with an initial square microchannel (30 μm × 30 μm), and the channel aspect ratio can be adjusted from 1 to 5 by external stretching. Next, the effects of aspect ratio, particle size, flow rate, and poly(ethylene oxide) (PEO) concentration that make the fluid viscoelastic on particle migration were investigated. Finally, we demonstrated the feasibility of our approach by testing channels with an aspect ratio of 3 for the separation of both particles and cells.