ip采用request.remote_addr获取
User-Agent采用request.headers.get('User-Agent')获取
代码如下

# -*- coding: utf8 -*-   

from flask import Flask, request
app = Flask(__name__)
@app.route('/')
def index():
    ua = request.headers.get('User-Agent')
    ip = request.remote_addr
    return ua,ip
if __name__ == '__main__':
    app.run(host="0.0.0.0",port=int("80"))

API接口

# -*- coding: utf8 -*-   

from flask import Flask, request,Response,jsonify
from datetime import datetime

app = Flask(__name__)
@app.route('/')
def index():
    now = datetime.now()
    ua = request.headers.get('User-Agent')
    ip = request.remote_addr
    data={
        'ip':ip,
        'User-Agent':ua,
        'time':now,
    }
    return jsonify(data)

if __name__ == '__main__':
    app.run(host="0.0.0.0",port=int("80"),debug=True)

运行结果