Unfortunately no integration is possible between the Tradfri gateway and SmartThings at this time. It is up to IKEA to make this possible if they want, and so far they haven’t.
(Note That you also cannot add the ikea gateway to a Hue bridge or a Vera plus hub.)
The Zigbee Limitation: Only One “Coordinator” Per Network
First it is important to note that the zigbee profile that SmartThings uses only allows for one primary “coordinator” per network. The ST hub is one. The Tradfri gateway is also one. So each of these expects to own its own network and to be the only coordinator on it. 
(Zwave handles this differently, and does allow for secondary controllers. But zigbee does not.)
Philips made the decision from the beginning that they wanted to handle this differently for Hue. So they used a completely different architecture. The Hue bridge does act as a zigbee hub for its own mini network of the zigbee devices that are connected to it. But it also has an open API which allows other systems to communicate with it, either cloud to cloud or LAN. Note that it does not use zigbee for these third party communications.
So: IKEA could have done that, but so far they haven’t. And probably won’t, as it would increase the cost of their own device. Note that the Tradfri gateway also doesn’t have an IFTTT service. (One reason the Hue bridge is more expensive is that it does more stuff.)
So: one zigbee hub per network, and the ST Hub is it.
As far as using Homekit with ST, there are two methods.
HomeKit method 1: HomeBridge
The first, as @sidjohn1 already mentioned, Is to use the “homebridge” emulator, which basically makes SmartThings look like a Hue bridge to HomeKit. You will need additional hardware and the technical setup is quite complex, but it gives you a lot of features, including individual control of most devices. The people in the thread he linked to can explain more.
Homekit Method 2: Siri Shortcuts
The second newer method which has only been available for a few months is to use Siri shortcuts. No additional hardware needed and it’s simpler to set up. But you basically have to create one Integration applet for each command you want to say. So it works quite well if there are only 3 or 4 voice tasks you want to share, but above that setup can get quite tedious. And it’s really a Siri integration, not a Homekit Integration. And it can have some lag.
So the shortcuts method should work fine for a few voice commands like “turn off all lights” at night, or “Hey, Siri, good morning.” But it’s probably not going to work for more granular controls or for automations.