The subject of cesium chloride has cropped up in various PCa groups over the years. Enough for me to be aware of it, but not of outcomes for those who tried it.
There have been no clinical trials of cesium chloride. Not for PCa, any other cancer, or any non-cancer condition. So there is little to go on.
Swanson & iHerb do not sell it, but it's easy to get hold of.
A 2015 paper  gives some background on why people use it:
"The alkali metal cesium is used as an alternative and complementary cancer treatment in the context of ‘high pH therapy’ . This therapy was based upon the hypothesized but never demonstrated preferential uptake by malignant cells of cesium cations in exchange for protons, purportedly retarding tumor cell cycle progression secondary to unvalidated intracellular alkalosis. Two uncontrolled, non-randomized case series suggesting potential benefits of cesium therapy were not confirmed by subsequent studies. Despite the American Cancer Society's explicit warning against cesium use
"unapproved ingestion of cesium has led to toxicity and death."
"Cesium shares its outer-shell electronic structure with sodium, potassium and lithium. Like potassium, cesium is avidly absorbed in the small bowel and secreted by the distal nephron. Cesium ingestion is associated with depletion of both intracellular and extracellular potassium. Cesium administration to rodents can model torsades de pointes, and human ingestion has caused prolonged QTc, torsades de pointes, ventricular tachycardia, and death. Cesium-associated arrhythmias are likely exacerbated by cesium-associated hypokalemia (CAH), which has been attributed to ‘cellular shift’."
This & other case reports    describe toxicity.
There was a 2010 review paper :
"The knowledge about cesium metabolism and toxicity is sparse. Oral intake of cesium chloride has been widely promoted on the basis of the hypothesis referred to as "high pH cancer therapy", a complimentary alternative medicine method for cancer treatment. However, no properly confirmed tumor regression was reported so far in all probability because of neither theoretical nor experimental grounds for this proposal. The aim of the present review was to resume and discuss the material currently available on cesium salts and their applications in medicine. The presence of cesium in the cell does not guarantee high pH of its content, and there is no clinical evidence to support the claims that cancer cells are vulnerable to cesium. Cesium is relatively safe; signs of its mild toxicity are gastrointestinal distress, hypotension, syncope, numbness, or tingling of the lips. Nevertheless, total cesium intakes of 6 g/day have been found to produce severe hypokalemia, hypomagnesemia, prolonged QTc interval, episodes of polymorphic ventricular tachycardia, with or without torsade de pointes, and even acute heart arrest. However, full information on its acute and chronic toxicity is not sufficiently known. Health care providers should be aware of the cardiac complications, as a result of careless cesium usage as alternative medicine."