I'm going to interject here and i hope that Golthing will contribute too. It is widely believed among fasting experts that detox is most aggressive with the least amount of water intake and most instruct their patients to drink only when thirsty. There are various reasons behind this, one of them being that the kidneys are given as much of a break as possible, but personally i believe there are much more substantial reasons.
Dr. Filanov a Russian dry fasting expert who has supervised thousands of dry fasts, often up to 14 days states and i paraphrase that, "dry fasting creates an environment whereby cells act like miniature furnaces burning up toxic materials".
He also states that, "Dehydration causes competition between healthy cells and pathological organisms for water. It is a real survival-of-the-fittest scenario. Inflammation cannot survive without water. A wet environment is ideal for the proliferation of pathological bacteria, viruses and worms – water shortage is as devastating as fire for them. All dead or dying tissues will be expelled from the body. A water fast does the same thing but takes much longer to accomplish the goal."
"What is inflammation? Tissues are swollen with water where infection is having a party. Pathological bacteria and microbes love wet terrain. Dry fasting eliminates inflammation the same way a swamp gets rid of mosquitoes and other insects when it dries up. Microbes are annihilated immediately. The shortage of water is a cleansing drought that is disastrous to the body’s enemies. It is pernicious for pathological bacteria."
Note that the water is not as limited as people might imagine, largely because a fasting body produces about 1 or 1.2 liter of metabolic water through hydrogen being released as a bi-product primarily from metabolized fat combining with oxygen breathed in from the air (forming pure h2o).
To address your specific question, "how does detoxing work when the kidneys are not receiving enough water"... i believe that as long as a person is not experiencing thirst (and i would say a fairly substantial level of it that becomes difficult to ignore rather than the mere initial hints of it), there is definitely no shortage of water provided to the kidneys to enable them to perform their function. To give you a personal example, i recently dry fasted for 5 days and i was urinating 3 or 4 times per day even towards the end of this, even as thirst began to become uncomfortable in the last several hours. A person who needs water will certainly receive a strong signal in the form of thirst as soon as it is needed even as i have in the past at a much earlier place.
Your other question, "how long can one go without water" has a widely varying answer. For one person this might be 20 hours and for another it might be 14 days (or even longer in extreme instances). A lot of factors come into play here one of which is the level of toxicity. Greater toxicity, less ability to endure a dry fast.
One more amazing dry fasting tidbit that i want to borrow from there is as follows:
"Experiments on rats have tested the effects of fasting on the immune system. Filonov talked about an experiment he observed at one medical school: 120 white rats were divided into four groups of 30. All were injected with sarcoma (a cancer of the connective tissue). The control group ate regularly, while the other three groups were placed on a 3-day [Dry] fast at some point in the experiment. Of the group of 30 injected with sarcoma prior to the fast, half died. The second group, injected during the fast, had a 1/3 death rate. In the third group, injected immediately after the fast, all the rats survived. The rats in the control group, which did not fast, all died.