From Fox Road Marina (where my boat is) to Watts Bar Dam, it takes roughly 5-6 hours depending (*downriver with the current*)....From Watts Bar Dam to Chickamauga Dam, you're about another hour or so.
Now, i'm about 45 mins (by boat) from Fox Road Marina to Neyland. Depending on where you're at on Chickamauga, I would probably account for 10 hours or so depending on lock times, etc.
For fuel on Watts Bar coming up river from the dam, you have Euchee, Blue Springs, and a couple of other's. I would probably fill up at Blue Springs, from there you're about 2-3 hours from your last lock up which is Ft. Loudon. On the other side of the dam from Ft. Loudon, you immediately have another marina and a Calhouns!!
Going up from there you have Choto, International Harbor, Concord Marina, Fox Road, Louisville Landing, and finally Volunteer Landing.
Gas won't be a problem as long as you plan it correctly. Do you have a GPS?
I have a handheld Garmin, I routed the trip out (the first time I took it about 3 years ago) with Garmin's software on my laptop and then loaded that route into my handheld. I had to use waypoints on the software to make the route on water and not land. I used mile marker buoys as waypoints. It's always nice to know you're coordinates in case of emergency. I would also go buy a handheld ship to shore if your boat doesn't already have one.
I would not make the trip without a ship to shore radio......Good Luck, you'll be fine!!