Попробуйте gevent:
from flask import Flask
from gevent.pywsgi import WSGIServer
app = Flask(__name__)
@app.route('/api', methods=['GET'])
def index():
return "Hello, World!"
if __name__ == '__main__':
# Debug/Development
# app.run(debug=True, host="0.0.0.0", port="5000")
# Production
http_server = WSGIServer(('', 5000), app)
http_server.serve_forever()
Примечание. Установите gevent, используя pip install gevent