"thence N 14°35'40" W 561.45 feet generally with the said branch" could be read one of two ways if it ever needs to go to court.
Place a comma before "generally" and the bearing and distance hold over the creek location. Place it after "generally" and the creek is the boundary.
Someone else said that if both sides are still in the family, ask them and hope you get agreement. document the answer and survey accordingly.
If you are going to rewrite the description to make it clear the creek is the boundary, make sure you include precise language to make that intent clear so that 30 years from now there isn't a surveyor asking "Is the creek the boundary or should I hold these twelve courses?".
The way I would write it would be... "... Thence along the center of said Kirkham Branch as approximated by the following twelve (12) courses: 1) N DD°mm'ss"W, xxx.xx ft, 2)... ; Thence leaveing the center of said Kirkham Branch..."
I don't like the word "generally" used in the description, but it's to the centerline. My 2 cents.
However...following intent is the goal, and you have the rare (at least for me) opportunity to get a definitive answer regarding intent from the owner(s) since both parcels are owned by the same (or at least mutual) interest. Ask the owners what they intended. Now, if dear old dad split the property and put both pieces in the estate but is now dead, you can still ask the current owners (members of the estate) and get a reliable answer on intent or at least the basis for a boundary line agreement. I think your last important step would be to write updated/modernized legal descriptions for both parcels that will provide sufficient language to clear this issue up, AND coach up the owners on how to get the descriptions on record.
Personally, I don't have a big problem with the legal...but is could be written a little better to say the least.
Removing Ambiguity is my goal.
Nate