Generally, we do not encourage the addition of cleaning agents to your rain barrels and tanks. If a system is properly installed with screens, filters, and sediment traps, it should not need routine cleaning, or any additional chemical warfare. The tank has a healthy biome that you do not want to kill. Moreover, chlorine can interact with and damage the plastic tank, depending on the concentration and exposure time. Chlorine is added in a concentrated form and then diluted - during that concentrated time, more harm can be done than good. Instead of adding chemicals, here are some recommended ways to maintain tank health and cleanliness.
Leaf Eater
A leaf eater is a simple and effective way to keep gutter debris from entering your rain barrel, and are easy to install and maintain.
Light Guard
This depressed Solar shield is installed right under the mesh basket on your rain barrel. This reduces UV in the tank, and helps prevent algae growth.
If you absolutely must:
You can try mixing 1/4 cup to 2500 gallons. Yes, this is very diluted (You're not trying to disinfect with the bleach). If you are going to dose your tank with bleach, go low and slow with liquid household bleach.
Use only plain, unscented household bleach (do not use splashless, scented, or color-safe bleaches). It must contain between 3.0% and 8.25% sodium hypochlorite.
NEVER put powder or tablet forms of chlorine in your tank, that would sit directly on the tank until they dissolve.
For algae, chlorine is dramatically superior to hydrogen peroxide. Using household bleach (sodium hypochlorite) can be a short-term method to kill algae and bacteria in stored water or tanks.
Hydrogen peroxide is not a good disinfectant, but an excellent oxidizer. Contact time dilutes its ability to oxidize. Therefore, you do NOT want to use hydrogen peroxide with a retention tank. Only use in flowing systems.
Removing iron and sulfur is best accomplished with oxidation. If you have incredibly high iron or sulfur, chlorine is not a good choice, but hydrogen peroxide is. An H2O2-injection system would be needed to properly administer hydrogen peroxide for iron and sulfur eradication.