I feel like I'm piling on, but I have 40 yrs experience with T/C rifles and manage to enjoy them without the "issues" that can arise from their "patent breech" design.
Mike Brooks has it right. The symptoms you describe are absolutely what you expect to see when "stuff" has made it's way into the reduced area between your main charge and the ventliner.
Your report says
"the first few shots went off splendidly, very quick ignition. Then it began to delay and finally turned into a hang fire"From that, it appears that there wasn't anything major wrong with the rifle when you got it and that the problems you're having are related to what you're doing at the range.
Jumping ahead to cleaning...I'm a big fan of the "pumping method" Mike mentioned. The good folks at T/C built those rifles to make them easy to clean so take advantage of it. Pull the barrel, pull the vent liner and go to pumping a solution of hot soap and water through the barrel. Follow with plain water. Like Mike said...use a tight patch on your jag so you can get some force and water won't migrate over the jag.
At this point...I'm going to diverge from other's comments and tell you what I've been doing for 40 years, without a problem.
I'm one of those who finishes the water cleaning by pouring a cup of boiling water through the barrel...(you will want a thick piece of towel or pot holder handy). When the last of the water has run through the barrel...I IMMEDIATELY run a patch wet with Ballistol behind it. Then a couple more while the barrel is still warm. I've read all the comments and warnings about "flash rust" over the years. I'm not questioning other's experience, just sharing mine. All I can say is my original T/C barrels still look nice and shiny inside and still shoot REAL WELL.
I have a small bore light that. The tip kinda fits into the threaded hole at the vent after I've pulled the liner. When I check it from that end with the light, I can see the light coming in the the vent, through the "patent breech" and into the barrel and know that the reduced passage is clear.
On the topic of vent liners...A while back I stumbled on a T/C vent liner that works real well. It's T/C No. 7327. 1/4 x 28 threads as are all the T/C barrels. They call it a "Flintlock Touchhole Bushing". It's coned on the inside. The outside is also sort of "coned" in that it has a 1/8" hole to allow for the use of a 1/8" allen wrench for removal/installation (included). It's not very "traditional", but it works great when reliability is the first priority. I use on in my flintlock hunting rifle. It's a 50 cal T/C "Hawken style"
I don't have any issues with delays or hangfires on that rifle. .
Sorry to be so wordy...it's early and I tend to run on.
Get that rifle clean and get it back to shooting without delays and hangfires...then we can work out how to keep it that way.
Hope this helps.