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Here are the steps to exhibit a color palette on a website using Flask and KMeans clustering that consists of the most commonly used colors:

1. Collect dataset: Collect a dataset of images that represent your website. These could be screenshots of your website or images related to your brand.

2. Extract colors: Use a tool like Python's Pillow library to extract the most dominant colors from the images in your dataset. For instance, you can use the ImageColorz library that implements KMeans clustering to extract the colors.

3. Obtain the most common colors: Once you have extracted the colors, use a function to find the most commonly used colors in the dataset. One way to achieve this is to select the top N colors with the highest frequency.

4. Store the colors: Store the most common colors in a data structure, such as a list or dictionary, and pass it to the Flask app.

5. Create a web page: Create a web page using Flask that displays the color palette to the user. You can use HTML and CSS to format the page and display the colors.

6. Add interactivity: Add interactivity to the web page. For instance, you can enable the user to click on a color and copy its code to the clipboard. This can be achieved using JavaScript.

7. Deploy your app: Once your app is ready, deploy it on a web server so that it can be accessed by users. You can use a service like Heroku to deploy the app.

By following these steps, you will be able to create a web-based color palette that displays the most commonly used colors for your website.