The Problem

Cystinuria is characterized by the inadequate re-absorption of Cystine in the proximal convoluted tubules after the filtering of the amino acids by the kidney's glomeruli (located in the glomerular capsul also known as Bowman's capsule), thus resulting in an excessive concentration of Cystine in the urine. 
To make something clear, the issue with Cystine is not that our dogs bodies are flushing it all out, rather than flushing a high amount of it. A percentage of Cystine is absorbed by the body.
This means that if a cystinuric dog has 5000mg of Cystine in its system it will not all be flushed to and through its bladder, but only a percentage of it will, this being a significant one. A percentage of Cystine will stay in the body and be used for its needs.
So how much will it flush ?
This depends on the total amount of Cystine that is consumed resulting in the excess (for a cystinuric dog) not being able to be fully absorbed and used by the body, and since our dogs have the issue of incomplete absorption a lot of this Cystine is going passed proximal tubule and into the bladder where it will be passed through the urine.

The problem with having to much Cystine in the bladder is that until it is passed through urination, it hovers in the bladder and forms hexagonal shaped crystals that can be viewed upon microscopic analysis of the urine. The crystals typical of cystinuria are able to form stones by grouping together. This is possible with the help of high levels of uric acid in the urine, also known as a pH levels in urine.