This is likely tied to general game lag.
Try using the following link to access the game
https://cdn.megaplanetgame.com/web/static/game_files/MegaPlanet.html in fullscreen mode using F11 on your keyboard. If this doesn't work use the key Fn + F11 simultaneously.
It will eleviate some issues with chat being slow but it will not be eliminated, rooms with many animated items or that have the rare/gold collection shimmer effect tends to slow down the text chat box.