Bach flower essences are bunk, and so are many of the products out there. I have never seen a single decent un-biased study proving the effectiveness of Rescue Remedy. I think it's mainly placebo effect, and effects of the alcohol in it (if enough is consumed).
Some of the other "calming" products may have some
effective ingredients in them, but use too little dosage to actually be effective. Valerian root is commonly taken for insomnia and anxiety/stress (and given to dogs), but there's also no proof it helps with anxiety. Anyone giving their dog herbs has to read up on any contraindications or potential health effects like liver issues. Just because it's "natural" does not mean it's harmless!
For calming, a few things: DAP
(Dog Appeasing Pheromone) is proven to be effective in some dogs. They have diffusers, collars, and a spray you could put on the dogs bedding or on a bandanna. Melatonin
is something to look into, and has been used with success for anxiety. Lavender essential oil is supposed to have a calming effect. I'm not sure if aromatherapy is truly effective, but at least it's harmless and smells good. Another product I recommend is Composure by VetriScience, which contains L-Theanine
For humans with anxiety, diazepam or alprazolam
While medication is often effective for both dogs and humans... this is the natural health section. If you want the natural route, there's Valerian root again, there's a product I take called Busy Brain that contains B-vitamins/L-theanine and is supposed to help support focus and calmness without drowsiness- Busy Brain Release?
. Also exercise, yoga, meditation, music.