A lot of the higher end foods have flax, so maybe you should try one without the fish first and see if that does it. Usually, if a dog has trouble with flax, it will show itself by causing itchiness, not usually loose stool...
Canidae makes one with just chicken as a protein source (but it has flax):
Canidae Chicken and Rice
The Wellness "Simple Solutions" brand also uses one protein source and one carb source, but it has flax too...
Wellness Simple food solutions