I would not use that solution to clean my radiator. Remember that a radiator itself is primarily made of fairly thin aluminum. The bleach/vinegar could very easily damage the structure and weaken it. A washing machine is made of (in most cases) a steel drum coated with porcelain, or stainless steel, both of which are very sturdy and are made to last a long time through a lot of abuse. Your car radiators only jobs are to maintain internal pressure, keep sealed, and allow the transfer of heat from your coolant.
A much better idea is to utilize one of the many products on the market which will safely clean your radiator for you, such as Gunk, Prestone, or Bar's Stop Leak flushes (there are many more, these are just examples). Following their directions here will save you not only time, but money as well. Using the above cleaning agents may, or may not, have adverse affects, but why chance it when you can utilize a product which is specifically designed to clean your entire cooling system and will not harm it in the process.