How did your repairs work out? Did this solve your problems?
As you can see from the responses here, today's chinking products can work very well in this situation as long as the movement isn't too excessive. Triple Stretch Chinking is a good choice as well. http://weatherall.com/chinking/triple-stretch-chinking/
However, our Mortar Match product is designed specifically for this application as Scott says. It is a cousin of the Triple Stretch product but has a little different formula that allows it to stretch better.
Hope you can close the gaps and prevent the air and water from causing bigger issues.
I think one of the best products that I have found for chinking between the logs and the chimney is a product called Mortar Match by Weatherall Co. It is a very high performance textured caulk with a heavier aggregate that gives the appearance of mortar. If the gap is small enough I will lay a ½ “ bead of Mortar Match on the seam between the mortar and the log. I will sometimes put a slight skim coat on the mortar joint just to stabilize it if it appears to be loose or cracking. The best color I have found for this application is “Southern Grey” It is a dead match for most mortar although almost any grey will work as it will eventually blend in with the mortar joint over time. I use this on chimneys, log fireplace mantels and wherever rock work meets with the logs. It can also be used as a high performance tuck pointing material between stone veneer and faux stone panels. If the gap between the logs and the mortar is fairly wide I install backer rod or expanding foam and go over the gap with the mortar match product. For more information on this product click on link below
If you need samples or have questions on application you can contact me at email@example.com.
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