How to use @p without command block?
Your command can be run by typing it into chat. No need for a command block. Your command will work as is, with the @p target selector.
I recommend you use @s target selector as it will select the player who executed the command, which is the player who clicked the tellraw text.
Note: The command is executed by the player at the permission level of the player. If your players do not have permission to use the kick command, your command will not work. There is a work around involving the trigger command but it adds complication to the system which will no longer be a type it in chat solution.