While my pump's lid almost always traps a few small bubbles, if I saw the amount of air you're describing I would assume there's a problem. It would be unrelated to my solar panels, except perhaps as Mark describes: the flow rate changing is just revealing some upstream problem. My flow rate would go down when my solar kicks on, that would be expected behavior, except my automation controller automatically ramps up the flow rate when solar heat is called for, so I don't actually see the flow rate drop. Regardless, my solar kicking in doesn't, and shouldn't, draw air into my pump.
The first time my solar heater comes on each day, the empty panels fill with water and a lot of air is pumped out of them. The air ends up in pool as quite a display of a lot of bubbles coming out of all of my returns. Not quite jacuzzi level, but enough to get waves going and make a decent racket. If the heater turns off and on throughout the day, this filling process is not repeated. My panels remain full all day, whether they're heating the pool or not. Then, at the end of the day, when my filter pump is finished and turns off, the panels drain all but a small amount of water back into the pool. The water is displaced by air that is sucked in through a vacuum breaker installed near my roof. It sounds a bit like a frog croaking. So that's why the panels are empty the next morning, and then the whole process repeats each day.
It's my understanding that my setup and the way it works is a typical solar heater installation. There are other ways to make it all happen, so it's hard to say from your one pic if that's how your setup would work. One thing to watch out for, because I see you have a chlorinator, is that the output of the chlorinator should not feed into the solar panels. Water for the solar panels should head to the roof and then return to your plumbing in between your filter and your chlorinator. So that's something you can double check. Or provide more pics from several angles of all your plumbing.
I determined the optimum flow rate for the type and number of my solar panels by referring to the panels' installation manual. The optimum rate for one is 5GPM. I multiplied that by the number of panels to get the flow rate: 8 panels x 5GPM = 40GPM. I replaced the "guts" of one of my check valves with a FlowVis flow meter, and then it was a very simple matter to adjust the RPM of my variable speed pump to achieve 40GPM. That's it. I know that my panels are heating my pool as cost effectively as possible. As Allen points out: too little flow will not heat the pool as well as it could be, and too much flow will just cost more in electricity without a corresponding increase in heat.
As Mark points out, there are other ways to calculate your flow rate. He gave you some simple math, along with an alternate method. Some installers just feel the solar heater output at a pool return and if the return water is slightly warmer than the pool water, then they're done. Mark gave you that 5°F number, that's about right. It's often misunderstood that by reducing the flow (RPM), which results in warmer water out of the return, that that is good. But the physics of heating a pool dictate that it's better to move a lot of water that is a little warmer, then less water that is a lot warmer.
Anywho, I didn't want to rely on guessing, or feeling, or estimating with math, I wanted to make sure my flow rate was dead on. And so I went with a flow meter. I also use that meter to adjust flow for my cleaner, and my SWG and I monitor it throughout the year to adjust flow rates as they drop due to the filter slowing things up as it collects dirt. So I get good value from that purchase, and my solar heater is as efficient as it can be...