Deuce50-I've built more than 50 Hawkens, three flint and some from a blank. My first advice- forget working a blank, you don't need that misery. Get Track's stock HS-16-M1 for $84, which is shaped and inlet for 1-inch barrel only with 7/16" rod hole drilled. It is in stock as of now. They do have that in 15/16" barrel channel, but "expect 30 days". I think they get stocks from Pecatonica and I have had the above stock (M-1, plain maple) ordered from them since March 12 and have no idea when I'll get it. Are they even working?
Second- go with a one-inch .54 barrel, they have a 36" Green Mountain in stock. Cut it to 32" or 31 1/8" like the Carson Hawken. Why the 1"? Because the breech plug and tang that is best for a flint Hawken is Track's Plug-FHG-16-3, with 3/4-16 threads. You cannot fit that to a 15/16" barrel because they are tapped for a 5/8-18 plug. Unless you as a machinist want to cut the breech off and drill and tap it 5/8-18- but you are at home. (The 1" plug can be filed down to 15/16", I did that with a 15/16 H&H barrel tapped 3/4-16, for a light Hawken). Track has all the parts in stock that you'll need.
Third- do not get Track's Hawken plans- they are out-sized, 14 5/8" length of pull, etc. See my gun building posts about this. Just click on my name and choose "show posts by user" and 40 some pages of my posts come up. I replaced all my gun building photos, so you should find useful tips in there somewhere.
If you want, I can copy my Green River Rifle Works Hawken halfstock drawing and send it to you with a list of all the parts you will need. All the parts are available at Track as of now. You'd be making a basic GRRW or Carson Hawken but in flint. That shape and size rifle works very well, it is my favorite.
Costs you $10 for copying and postage, if you want. PM me if so.