Kali Linux does not use the BurpSuite installer, rather it uses the Burp Suite JAR file.
The JAR file is kept in the /usr/bin folder.
Click on Download the latest version.
Ensure, you select JAR and click Download
Save the file to your Downloads folder
Navigate to /usr/bin
Rename burp suite to old
sudo mv burpsuite burpsuite_old
Copy the last burp suite jar file to /usr/bin
sudo cp /root/Downloads/burpsuite_community_*.jar /usr/bin/
Rename the new jar to burpsuite
sudo mv burpsuite_community_*.jar burpsuite
Give permissions to execute the file as program
sudo chmod +x burpsuite
Delete the old BurpSuite File
sudo rm burp suite_old