A friend of mine is wanting to do a specific build and as far as I am aware you cannot apply a modifier multiple times in this way. Can someone confirm if this is a RAW legal tactic?
level 6 tiefling celestial warlock, with 16 charisma (so modifier of +3).
Cast shillelagh to make staff 1d8+cha [source: pact of the tome]
Then cast searing smite for 1d6+cha [source: tiefling and celestial warlock's radiant soul feature to add charisma mod]
Then green-flame blade attack for another 1d8+cha [celestial warlock's radiant soul feature to add charisma mod]
A single hit would be 2d8+1d6+9
Do all these instances of charisma modifier stack like this?
Your friend is right, mostly
I'm assuming a Zariel Tiefling.
Casting shillelagh on your quarterstaff changes its damage die to 1d8 and allows you to use CHA for attack and damage.
Casting searing smite at 2nd level means that the next melee weapon hit adds 2d6 fire damage (not 1d6 as in the question) to the initial hit, and the target takes 1d6 damage each turn until it saves or puts out the fire. There is normally no CHA modifier here, but the celestial warlock has the Radiant Soul feature, which adds the spellcasting mod to one damage roll, so, the initial hit (not the subsquent rolls) is 2d6 + cha mod.
Casting greenflame blade at 6th level requires you to make a melee attack with a weapon. If you hit, this will do 1d8 + CHA Mod bludgeoning damage (the weapon) + 2d6 fire damage (searing smite) + 1d8 + CHA mod fire damage (greenflame blade, normally no CHA modifier here, but Radiant Soul applies again, since it is a second spell). A second target takes 1d8 + CHA mod fire damage (greenflame blade).
Total damage: 2d8+2d6+9 to the first target and 1d8+3 to the second target.
You can move the Radiant Soul CHA mod around in the casting of greenflame blade, making the damage 2d8+2d6+6 and 1d8+6.
Thanks @Clarus_Nox for pointing out the Radiant Soul feature I had missed. Without that note, my answer was wrong.