Unable to get Thingspeak to display multiple fields in a channel using webhook/web form

Do you have your API_writeKey defined in your webhook for the particular channel you are writing to?
If not, or you want the ability to send to various channels, you will need to also send "k" for the channel's API Key in your Publish.

Here's an example:
See post #14 and the webhook definition below it.

Or you can use the ThingSpeak Library, as previously mentioned.