Dear Pretty Kitty,
The answer to your problem comes straight from the famous pet writer Curl Barks.
You must SEIZE THE MEANS OF PRODUCTION!!!!!
First you need to find the cowgirl your master is getting all this milk from, then you should emancipet her immediately (literature for this purpose can be found in any Snuggle Struggle base should you need it). Once the cowgirl responsible has been converted to our cause and set loose from her halter to roam in glorious fweedom, your master won't be able to give you milk anymore!
Your master may initially be upset with this, believing he has failed in his duty to you. If so, you could distract him by licking and batting at his man-penis. This tends to divert any master's attention completely.
Love and yips,