Want to clear ingame chat quickly? Then if you play MC 1.9 and above, you can use the ingame keybind:

f3 plus d

(Do not press +/plus, just f3 and d on the same time.)

If under 1.9, you could for 1.7.10 use something like https://www.curseforge.com/minecraft/mc-mods/clearchat which does the same thing just by pressing delete button.