It's a valuable idea to think that a Linear supply will be less noisy and much better performance.. 

However this thinking doesn't apply to all products and not 100% sure if you'd hear the improvements on a Flex knowing our extremely low noise floor (128dBA SNR). 

The second concern would be the possibility that a linear power supply could introduce a whole lot of issues with ground loops as it is commonly the case when you add a linear supply to an audio chain. 

While you might think, a wall wart = cheap electronics, ours was very carefully selected for its very low noise floor among more than 40 models and most importantly customised together with the manufacturer to achieve the best performance. Bottom line: Don't get fooled by its appearance.. Have a listen and notice how good the Flex is already out of the box!