I'm not familiar with a Hatfield so when it comes to cleaning you may need to take bit more care.
The first thing you need to know is whether or not it has a patent breach or flat breach. Second, does it have a touch hole liner and not just a drilled touch hole. Third, if it has a liner is it the type that can be removed. Forth, is the barrel pined or does it have a "hooked" breach and wedges so it can be removed. (this also applies to cap guns but I digress)
If it has a patent breach and a touch hole liner that can be removed I'd strongly recommend that you remove it when you clean so you have good access to the Breach since the best you can do down the barrel is clean the false breach. If it has a patent breach and a drilled or non-removable liner then clean the best you can and remember that you have a cavity below the false breach that you have to also get clean, dry, and greased/oiled.
If the barrel comes off ie. has a hooked breach then take it off put it in a bucket of your cleaner of choice and have at it this will get the barrel and patent breach clean you just have to remember to get it dry.
If the barrel is pined and you have a removable touch hole liner you can get a threaded flush tube you can put in its place and use it to flush cleaner thought the barrel and breach with the barrel on the stock and you can dry and lube it through the hole the liner goes in. If it does not have a removable liner you may want to try a clamp device that fits over the barrel and covers the touch hole so you can flush it as I said before.
Having said all this probably the most important thing about cleaning a flinter is knowing how you gun is designed. But, that is true of all muzzleloaders.
Before I forget, one other thing. Remove the lock regularly to make sure there is no build up of dust, powder, lint, or what ever in the works and that everything is still tight and working properly. You don't have to take it apart just brush it off and apply a few well placed drops of oil and it should be ready to go. One last thing, It is easier to clean the foot of the frizzen if you take it off the lock just be careful of the spring and don't squeeze it tight or you could break it.
Care for it well and it will serve you well.
