No, you should not give slippery elm bark (or any other human medication, supplement or herbal remedy) to your dog. In this particular instance, slippery elm bark is known to decrease the absorption of prescription medications (such as HeartGard or other heartworm preventatives). Also, many herbal remedies are only loosely regulated by the FDA in the United States and there are no tests for safety or efficacy before a supplement is marketed. There is no way to know what side effects your dog may experience from this, and the side effects in humans are often different from the side effects in animals.
Poop
Burdock root, sheep sorrel, slippery elm bark (inner bark), turkey rhubarb.
Slippery elm and black cherry bark, leaves and berries
One teaspoon of Slippery Elm Bark powder thrice a day.
Fish oil (especially Cod Liver Oil) is good for your cat, but phone the vets and ask how much you can give them. You can get those little syringes to measure it by and mix it in your pets food. This is also good for dogs. I wouldn't get too fancy with your pet because it can upset their digestive tract. In responding to the slippery elm aspect of the question, it is considered safe to give to cats. I'm not sure about the glycerin, but I don't know that it's necessary. Slippery elm has wonderful anti-inflammatory qualities, and is very soothing to the intestinal/digestive tract. Author Anitra Frazier gives the following recipe for Slippery Elm Bark syrup in her book, The New Natural Cat: Into a small saucepan place 1/2 cup cold water and 1 teaspoon powdered slippery elm bark. Whip with a fork. Bring to simmer over low flame, stirring constantly. Simmer 1 or 2 minutes or until slightly thickened. Cool and refrigerate. Keeps 7 or 8 days. Give a teaspoon of syrup (5 cc) for an average-size cat (again, about 10 pounds) 5 minutes before a meal to minimize diarrhea, or to soothe and heal mouth ulcers.
Slippery elm translates to Portuguese to become olmo.
The Hindi name for slippery elm is "अथेला" (Athela).
The Tamil word for slippery elm is சளியமரம் (chaḷiyamaram).
In Ayurveda, slippery elm is Ulmus rubra Muhl. However, it is native to North America so it is commonly known as Slippery Elm.
Slippery elm is called "गुळवेल" (Gulavel) in Marathi. This tree's inner bark is often used for its medicinal properties, particularly for soothing digestive issues and throat irritations. In traditional medicine, it has been valued for its demulcent and anti-inflammatory effects.
The Slippery Elm tree has been used by Indians for centuries. Only the fibrous, inner bark is used. It is used in cough syrups and teas to soothe coughs and throats.
The Slippery Elm, Latin name Ulmus rubra, is a species of tree that is indigenous to eastern North America, from Florida out west to Texas and then north to southern Quebec. The Slippery Elm is also known as the Red Elm and Gray Elm.