@Electroman Is that the only Romex cable in the Switch Box? This is definitely a 3-way installation, yes? 
That cable with the black/red/white is the Traveler Romex -  there should be a second black one that is either the line from the breaker or the wire to the load 
i.e. there should be all three screw terminals (plus neutral and ground) connected to the HS210 
See the tutorial in the Stickies

@Electroman 

Where does the red wire go on the other 2-gang box? 

Since you only have that one Romex in the first box, I suspect that the white is not actually a Neutral and is the 'other' Traveler wire. This is not uncommon (although the installing electrician SHOULD have identified the white wire with tape if that was the case. 

If it IS a traveler (and not a Neutral) you cannot use the HS210 

Question - when you removed the 'old' switch - was that white connected to it? (and same for the second box incidentally) 

If the white wire WAS connected to the old switch it is definitely a traveler - dumb switches never have a neutral connected to it. 
(It's always a good tip to take images of your original setup before you disconnect that you can refer back to - maybe bit late for that though) 

I need to study that second 2-gang box better - can you remove the other switch so I can see all the contents of that box? 

For the HS210, all the termninals need to be connected - one line/load (the common) and both Traveler Wires. 

@Electroman So if all the wires were indeed connected to the original switch at the single-gang location, then indeed that white is certainly a traveler. 

That centre switch is also a 3-way, but presumably a different Light circuit? 

On the Romex that is connected to the HS210 in the 3-gang box, it appears that the red wire goes over to a wire-nut - I presume that must be the Line Voltage 
So that would suggect that the Switch in the single box is your line end box - the red is actually the line voltage and the black and the white are the travelers 

So the big question is what to do .......... 
A prelimary question would be - is it critcal that you maintain physical control of the lights from both switch locations? (i.e. ability to manually turn the circuit on/off from both locations)? 

If you plan to use mostly by Smart Control (voice in Alexa ot from app) then it's easiest just to convert to single-way operation 

Or - I can give you a suggestion for an alternative device that does not require Neutral to utilize 3-way control - if you want to go that Route, send me a PM and I will respond with details privately (this is the Kasa forum after all) 

One quick post-script edit - in the marked up image I designated the second circuit with the 2-conductor wire as the load end and the switch as the load switch - that is not necessarily the case, it COULD be the Line end - you would have to measure the voltage on that to see which ) 

But for the circuit in question, I think I have it correct. 

@Electroman 

This is what I THINK your wiring is on that circuit in question 

Electroman wrote

 

Am I correct that the wiring for the HS210 in the 3-gang box is currently correct then?

 

and the issue is in the 1 gang box because I technically do not have a neutral?
 

@Electroman No unfortunately neither is correct (again the white is not neutral) -  it would be possible to install a smart switch in the 3-gang box, but you cannot wire it up a traditional 3-way circuit. 

I think this should work however 

(note - this is on the presumption that the Red Wire in the Traveler Romex is currently connected to a common incoming Line Voltage) 

So if you can reconfigure accordingly - just use the original dumb switch in the single gang location and at the 3-gang box you need to tie the Neutral from the HS210 to the one from the incoming Line Supply