Daryl,

this is one of the rifles I dreamed of!

I cannot tell about barrel details, loads or ballistics of the flintlock Jaeger rifles, or how they evolved until the end of the percussion era.
But I have the reprint a book from 1877 describing these things at length. You may say this is the summary of knowledge accumulated until then. I hope you will enjoy this.

Title is "Die Jagd-Feuergewehre" (The Hunting Firearms), author Adolf Zimmer, gun dealer in Dresden.
Thanks to Lancaster for recommending this book to me some time ago.
A first edition of the book was published in 1869, and this is the second, revised edition.
It covers muzzleloading rifles and shotguns, and then all the breechloaders in use, for pin fire, needle fire and Lancaster cartridges.
The chapters on barrels, sighting-in etc. appear focussed on muzzleloaders. Different loading methods are compared: patched ball or elongated bullet, bullets which are upset during loading, Minie bullets etc. The patched bullet is still preferable for hunting rifles. Loading may take a bit more time, but precision is the best to be obtained. Expansion bullets need length for good sealing and are then too heavy for hunting purposes. The author says that pin fire rifles use similar barrels and bullets as muzzleloaders. Lancaster rifles are very new, and Zimmer doubts that they will succeed, he prefers the Lefaucheux system.
It's funny that the new German military rifle M1871 and the .43 Mauser cartridge are not even considered for hunting. Mr. Zimmer certainly knew his trade, but he erred in his predictions for the future - or he was a bit conservative.

On bullets:
caliber between 13.5 mm and 14.5 mm (.53 to .57''),
bullet weight between 18 g and 25 g (278 to 386 grains).

Bullets with a flat or rounded tip are preferred over bullets with a sharp conical tip, because they are much more stable during penetration, and because they give a bigger entrance wound - for this reason some hunters still use the old round ball.
Military rifles now have 10 to 12 mm caliber, with longer bullets of 18 to 25 grams weight. They certainly have better ballistics and penetration, but are not suitable for hunting because they lack in shocking power and the entrance wound is not large enough.

On barrels:
Usually 6 - 8 grooves, depth of grooves between 0.25 and .35 mm (.01 to .014'').
Twist shall be slow to use strong powder loads (and a fast twist reduces bullet velocity!). Short barrels need a faster twist. Barrel length for the now usual double guns is 65 to 70 cm (26-28''). For these, he recommends one turn in 108 - 116 cm (42.5 - 46'') for elongated bullets, a bit faster twist for balls.

On powder loads:
for the above recommended bullet a powder charge between 3 g and 3.5 g (46 to 54 grains),
ratio powder to bullet between 1:6 and 1:7.
He gives no detail on bullet velocity except saying casually: "bullet travels about 1000 feet in a second", and obviously thinks this is plenty. I translate this into roughly 1300 fps muzzle velocity.

On sighting-in: in general, one does not shoot with the rifle on game at more than 50 to 70 meters!
So the rifle should be sighted in zero at 60 meters. Thus bullet elevation at smaller distances is never more than 2 - 3 cm, and you can hold zero out to 70 meters.
Sighting-in at 80 or 90 meters will give considerable elevation at 40 or 50 meters. Estimation of distances and calculation of corrections by aiming low during hunting is a vile thing and often quite impossible!

Very detailed description of different front and rear sights, aiming errors and corrections of sights.
Shooting for sighting-in to be done over a shooting table, with sandbags as rifle rest.
If one wants to sight in very exactly it is recommended to do 20 shots. Then select the 10 best shots - the larger deviation of the other 10 shots is assumed to come from errors by the shooter! Divide the best 10 shots vertically and horizontally to find the center of the group.
With a good rifle, such 10 shot groups shall not be larger than 4 - 5 cm at 60 meters (1.6 - 2'' at 65 yards).

I would certainly like to compare all this to the book you have - Lt. James Forsyth, "Sporting Rifles and Their Projectiles" 1861

Fuhrmann