A soft flannel, like from an old flannel shirt works really well for final buffing.
I should think you'd have to hold it like you would for shining shoes, so you can obtain higher speeds and snap it for kicks.
I use carnauba wax and dremel wheels for the hard part, but I always go over the pipe one final time with flannel.
Dremel tools (or their equivalents) are OK but their rpm's are way way too high for a decent polish using Carnauba wax. Typically, even an adjustable speed dremel on it's lowest speed setting spins at about 15,000 rpm which is about 10x too fast to leave a deep shine on a pipe.
I recently replaced my adjustable speed hand drill but here are the costs involved to me.
1 x adjustable speed electric hand drill - $25
4 x 100mm Cotton loose leaf buffer wheels (for use in drill chucks) - $19
1 x 500g Green Tripoli - $8
1 x 500g White Diamond - $8
2 x 250 Carnauba Wax sticks - $4
Total = $64
Or you can buy a small tub of Halcyon II Wax for $5 and at a push you can also use Brown or Neutral Boot Polish (Kiwi is the best brand if you can get it in the States).
Failing all else, use an old cotton T-Shirt and tear into strips. Secure your pipe using what is to hand, and strop, the pipe using the cotton strips.
Another thing you can do is order a wondercloth off eBay for $2.50 and they work really good. If you also get some 0000 steel wool and lightly rub it out with it then use the cloth they will look great. Not as good as a buffing wheel, but vast improvement.
OK, once more I need to step in and be the voice of reason. All these guys have ok ideas but it takes far too much work, time and money. The answer lies in the rock poli you have stored in the basement from when you were a kid. Briar is as hard as a rock. Seperate the stem from the bowl, toss them in the rock poli and set it on medium for 3 hours and your pipes will come out glistening.
Don't have a rock poli? No problem. Take a 50 pound bag of sand, pop it in the drier with all your pipes and stems and after 1 cycle, your pipe collection will look like it just came from the store.
savinelli makes a stem polish.it is nothing more than an extremely fine rubbing compound.Most well stocked pipe stores will have and/or can get.After using this on the stem,you can put a small amount on your finger and rub the briar along the grain.Use Tre-Wax as a fini. Will take some effort but if you work at it 'it will work better than anything.If you do not have experience with a dremel tool-LEAVE IT ALONE
I ordered a miracle cloth for three bucks I thought it was worth a try. I didn't know if you meant miracle cloth or wonder cloth but the miracle says it's for cleaning and polishing an the wonder one only said it was absorbent.