Question on the possibility of higher rebirth for animals In the questions Why not kill animals to hasten their rebirth? and Do the same rules of Karma apply to animals? and others, it in part discusses how animals have a very difficult time to be reborn as humans, and stuck endlessly in a cycle as animals. As I understand it, because they are not capable of Meritorious Deeds on there own.  

However, it seems to be possible for humans to transfer some good Karma to them, which may improve their chances of a higher rebirth.

If it is possible, how is this accomplished? Take this case:

Let's say there is a housefly in my house. Of course I could just grab a fly swatter and kill it. However, I choose to take 15 minutes to wait for it to fly to the screen door and then let it out.  

If this provides some good Karma for me, can it be transferred to the fly which may be helpful upon its rebirth? Or am I the only beneficiary of saving it (or at least for not killing it)?
No, you can't transfer merits to animals. You can only do that with a class of Petas(hungry ghosts) called the 'Paradattupa-jivi'. Animals at best might hear some Dhamma, memorise it and as a result be born in a better place next life. But that is extremely rare. Animals don't get stuck endlessly in the animal realm. They can easily sink lower and get into more extreme states of suffering. Once their bad karma has been exhausted, a past good Karma may come forward to give them a better life.

There is a classification of Karma, according to the priority of effect:


WEIGHTY (GARUKA) KARMA.
PROXIMATE (ASANNA) KARMA OR DEATH-PROXIMATE KARMA
HABITUAL (ACCINA) KARMA
RESERVE OR CUMULATIVE (KATATTA) KARMA


Katatta Kamma are usually the Kamma done in past lives. So if #1,#2,#3 are missing, Katatta Kamma will get a chance to result in the next birth. But that is highly unlikely as animals mostly have habitual and proximate Kammas. So the chances are that they will keep sinking lower. But once you get into the Niraya, you probably won't be creating any new significant Kamma. Because you will be in a constant state of agony throughout the lifespan.