I am looking at getting a Kentucky long rifle or a blue ridge flintlock from cabelas for my first black powder. After I buy the rifle is it cheaper than shooting .223? Without any research I want to say yes but I don't have any facts to back that statement up.

It depends.  If you are looking at shot per shot there is probably not a lot of difference.  Seeing as you and only get off 4 rounds a minute with a smokepole and a lot more than that with an AR your hourly rate would be much lower with the Blackpowder firearm.

Tons of variables here.
Where can you buy powder (black or substitute) at the best price?
Shooting patch material ––-pre-cut, lubed patch or pure cotton fabric at the yard goods store.
Percussion caps or are going with flintlock? Chert can be knapped down to servicable flints. Costs nothing but time. Caps cost money.
Roundball or conical bullets? I cast my own, have been doing so for the last 25 years. Have enough lead to hold me for the rest of my life.

If God meant for man to shoot caplocks, he would have sprinkled the earth with caps instead of flint.    Know what I mean, Vern?

Over time its cheaper.
Getting geared up is expensive. A lot also depends on how much shooting you'll do. If you're just going to shoot a few times a year(<100rds) getting all geared up is not needed.
You don't need a bunch of high dollar gear either.  A powder flask, powder measure, a few small tools will get you started. Caps can be carried in an old pill bottle, balls, bllets in a ziplock bag.
Powder and caps will be your main expense.
Caps are approx. .05-.08 cents each. Depends where you buy them. Flintlocks of course bypass this but you'll need to buy flints too unless you learn how to knapp flints.
Blackpowder costs anywhere from $14 to $30 a pound. Powder, Inc sells it for less than $14 per pound but you have to buy a 25pound lot to get that price.
Shooting, say, a 50grn charge will get you about 130 shots per pound.
Balls and bullets are very expensive if purchased. Home casting is the way to go on this. Moulds, handles, casting furnace, etc all cost but the cost is up on the front end. Scrap lead can be picked up for little cost if you watch for it.
Patching can be made from old clothes.
Lube - can be made with a little beeswax and criscoe shortening or olive oil. Staright PAM cooking spray will work in a pinch.
Cleaning solvents - can be purchased but are expensive. Simple hot water works great.

BP is fun but it requires more work.

considering black powder or a substitue is about 12 bucks a pound gives you 11 cesnts per shot for powder alone. now if you are not going to cast your own balls it will be about the same probably. if you go full bore with casting balls and such it may be a bit cheaper but it is all about the experience not cost.

I've never put 200 rounds through a smoke pole in an afternoon.

Out of curiosity I sat down and done some math and came up with .35 - .80 cents per shot fired. I tried to factor in different powder charges, bullet vs. ball, caps vs. flint and so forth. I'm sure someone can come up with a more accurate estimate.

So I guess to answer your question no it's not really cheaper per shot, but like some posters before me have indicated that it does save money because you don't fire so many round in an evening at the range.

ML with the cheapest sabots (TC Sure Fire $8/20 @ WalMart) and a couple 777 pellets runs a buck a trigger pull. Better sabots and the very popular Blackhorn209 will run you $1.50-$2.

If you buy a smaokeless ML like Savage, you can halve that cost.

If you cast your own round balls using battery plates, use your ear wax for lube, buy 250lbs of Holy Black at a time, you can save some money.