This ended up working for me.

Re: Using HTTP POST with Twilio
INPUT
{
"uri": "https://studio.twilio.com/v2/Flows/##################################/Executions",
"method": "POST",
"headers": {
"content-type": "application/x-www-form-urlencoded; charset=utf-8"
},
"authentication": {
"username": "**********************************",
"password": "*sanitized*",
"type": "Basic"
},
"body": "To=%2B12223334444&From=%2B15556667777"
}
OUTPUT
{
"statusCode": 201,
"headers": {
"Connection": "keep-alive",
"Twilio-Concurrent-Requests": "1",
"Twilio-Request-Id": "##################################",
"Twilio-Request-Duration": "0.055",
"Access-Control-Allow-Origin": "*",
"Access-Control-Allow-Headers": "Accept, Authorization, Content-Type, If-Match, If-Modified-Since, If-None-Match, If-Unmodified-Since",
"Access-Control-Allow-Methods": "GET, POST, DELETE, OPTIONS",
"Access-Control-Expose-Headers": "ETag",
"Access-Control-Allow-Credentials": "true",
"X-Shenanigans": "none",
"X-Home-Region": "us1",
"X-API-Domain": "studio.twilio.com",
"Strict-Transport-Security": "max-age=31536000",
"Date": "Tue, 08 Jun 2021 14:04:24 GMT",
"X-Powered-By": "AT-5000",
"Content-Length": "707",
"Content-Type": "application/json"
},
"body": {
"status": "active",
"date_updated": null,
"contact_channel_address": "+12223334444",
"account_sid": ""**********************************",",
"url": "https://studio.twilio.com/v2/Flows/##################################/Executions/##################################",
"context": {},
"sid": "##################################",
"date_created": "2021-06-08T14:04:23Z",
"flow_sid": "##################################",
"links": {
"steps": "https://studio.twilio.com/v2/Flows/##################################/Executions/##################################/Steps",
"execution_context": "https://studio.twilio.com/v2/Flows/##################################/Executions/##################################/Context"
}
}
}