As far as I know, there is no API endpoint or comprehensive list of supported emoji/keywords available. I was able to grab the full set (including custom emoji for the workspace) by inspecting the Slack emoji picker using React Developer Tools (Chrome extension).
Here's an example (JSON):
...
{
"name": "beers",
"unicode": "1f37b",
"id": "E1f37b",
"keywords": ["bar", "beer", "clink", "drink", "mug", "ale", "food"]
},
{
"name": "baby_bottle",
"unicode": "1f37c",
"id": "E1f37c",
"keywords": ["baby", "bottle", "drink", "milk", "infant"]
},
{
"name": "knife_fork_plate",
"unicode": "1f37d-fe0f",
"id": "E1f37d-fe0f",
"keywords": ["cooking", "fork", "knife", "plate"]
},
{
"name": "champagne",
"unicode": "1f37e",
"id": "E1f37e",
"keywords": ["bar", "bottle", "cork", "drink", "popping"]
},
{ "name": "popcorn", "unicode": "1f37f", "id": "E1f37f", "keywords": [] },
...
Full dump (as of 12/20/2020, excluding custom emoji): https://gist.github.com/impressiver/87b5b9682d935efba8936898fbfe1919