I don't know if this is dependant on you having finished the game or not... (EDIT: It appears that the Hellstorm Flare will automatically be selectable from your Gadget menu after you have shut down all 3 of the Defense Turrets on the map)...
If you go to any Supply Point, open up the Loadout menu, and then go into the Gadget Menu, you should just be able to select the Hellstorm Flare from the bottom row, second from the left. After exiting the menu, you can activate the flare by hitting the
button on your controller.
The game seems a little picky about where you can deploy the flare as i kept getting the message 'Cannot perform action' every time i tried to deploy it right next to the Supply Point. Just keep moving about and spamming the flare, at some point it will activate for you. What worked for me was to go somewhere on ground level, near water/the shore and try deploying it there.