How to Capture Data from a Webpage in Arduino and Display it over Serial Monitor of ESP8266?
There are two basic things you are doing wrong:

Firstly your HTTP request is wrongly formatted.  You have:

GET /apps/thinghttp/send_request?api_key=689WYA85WW1VJSBA
Host:api.thingspeak.com


What it should look like is:

GET /apps/thinghttp/send_request?api_key=689WYA85WW1VJSBA HTTP/1.0
Host: api.thingspeak.com:80


Also you only need one blank line after your request, not 5 as you seem to have.

Secondly you are not actually doing anything with the data the site is sending you. You make the request with +CIPSEND= but then the response, which is in the form +IPD,&lt;len&gt;:&lt;data&gt; is completely ignored.  You need to use the SoftwareSerial's .read() and associated functions to receive that data into the Arduino so you can actually do something with it - like send it down through Serial.

Tips:


Look for +IPD, first
Read up to the : and interpret it as a number
You now now how many bytes to read from the data section
Read that data
Do something with it