This is mostly an anecdotal post, but I'll post supportive links where I can. Reiki has yet to really be studied in clinical settings, but people and animals (or the people who care for animals) who experience it on a regular schedule notice a difference, myself included.
In order to deal with daily stress & anxiety in a healthy way, we need to learn about the nervous system (it is exactly the same for humans and animals). Our parasympathetic nervous system deals with "rest & digest" functions of our bodies and the sympathetic nervous system deals with "fight or flight". These two systems do not operate at the same time. It's one or the other. The fight or flight response is great for wild animals, street/stray animals, and for humans... to some extent. We need to rely on this response in emergency events, of course, but outside of emergencies we rarely need it fired up. Yet, when we are stressed out our bodies automatically shift into this fight or flight mode. When there is a perceived threat, our body responds with all kinds of reactions: increased heart rate, hormones etc., when the threat is gone, things return back to normal. Except... what happens when we are in a constant state of stress? In dog training, you would call this "Trigger Stacking". And you bet the same thing happens to us humans. Essentially, when we or our companion animals are living in a constant state of stress, our sympathetic nervous system is always turned on, which means we spend less time with the rest & digest portion turned on. Long-term exposure to stress hormones can lead to a laundry list of issues, so it's important to try and find ways to soothe and calm our nervous systems.
There are a few things that help me and I've noticed that since incorporating them into my day, I get less stressed, or stay worried about something for a shorter amount of time and they include:
Yoga
Meditation
Self-Reiki
Staying well hydrated
If you didn't read the Mayo Clinic article above, other things that can help with stress management include:
Healthful eating
Getting enough sleep
Deep breathing
Massage
Volunteering
Maintaining healthy relationships/friendships
Hobbies, reading, listening to music
Seeking professional help, when needed
So, you might ask, where does Reiki come into this equation exactly? Well, simply put, it can be placed in the same category as meditation, deep breathing or even massage and yoga. For our pets, it would be similar to foraging, chewing on a bone, napping and/or other solitary and quiet enrichment activities. When you get an opportunity to relax or rest, your parasympathetic nervous system gets the opportunity to turn on. At the very least, Reiki can give you and/or your animal companion that opportunity. There are some references to past studies here on Reiki and mental health and reducing stress and anxiety so hopefully the scientific community starts taking these studies further.
Anecdotally, the main things I notice that tell me that the parasympathetic nervous system has been activated are: 1) in humans, frequently the stomach will start making noises and gurgling, indicating that those systems are fired up and doing their jobs; 2) people will often enter a comfortable doze (I've had this happen in 15 minute mini-sessions during a busy event); 3) in dogs, often they will rest comfortably (though sometimes they have a mind of their own and do other things) and; 4) once the dog has entered into a resting period, they will almost always have a big, giant exhale release.
When we can find daily (meditation), weekly (yoga) and monthly (Reiki and/or massage) practices that help our bodies slip into parasympathetic activity more often, we will find ourselves more relaxed, happier and healthier. We will find that we can rebound from situations quicker and are able to manage our emotional response better. These are far from a cure but they certainly are tools we can use to help get us into a better space and improve our over-all well-being.