I cannot go 30 miles without a flat. I can't figure out what the problem is I have Mavix CXP-12 wheels (20mm). I have relatively new Freedom ThickSlick 23mm Tires on the wheels. I've been using these inner tubes: Meetlocks® 700x18-23c. I weigh 165 lb.

I just keep getting flats, both rear and front. More often the rear. Sometimes I get flats twice on a single 20 mile ride.

I was inflating to 110 PSI, and I assumed these were pinch flats, so I tried going up to 125 PSI and that just made things worse. Then I tried running at 90 PSI and that didn't help either. I thought the spokes seemed a bit loose and maybe they were poking the tube on bumps, so I tightened all the spokes a turn and that didn't help. I replaced the rim tape and that didn't help.

The tires are not compromised at all. The rims have no burrs or anything like that and the rim tape looks perfectly intact. These are definitely some sort of pinch flat. The punctures are usually on the side or inside of the inner tube.

I was having this same problem on another brand of inner tubes (I forget the brand name). So I doubt that's the issue.

I have no idea what's going on. Is there an incompatibility between these 23mm tires on my 20mm rim that leads to flats? Do I need to have the wheels rebuilt? They look perfectly true to me.

Any pointers appreciated. My only guess at the moment is I need to get 20mm tires. But I'm worried that'll just be a waste of money.
I've had this exact problem.  I spent a whole lot of time removing the inner tube, patching it, etc...   All to no avail. I finally figured out that the side of a drilled spoke access hole was barely visible next to the rim tape.  When I'd inflate the inner tube, it would jut into that hole (depression) and get cut on the side of the drilled hole at the aluminum rim.  The fix was to get better (wider) rim tape, and carefully adjust it so there was a uniform overlap at the spoke access holes. 

I also figured out that is VERY difficult to patch a hole on the inner side of the tube.  You have to use a patch that is at least two times its width (long axis oriented along the rim...)

Good luck with it.  

Oh, and to help me in troubleshooting, I always label the fill port on the outside side of the tire (In my case I rotate the tire so the pressure rating is next to the fill valve. Then I use a paint pen to add a tick mark on the sidewall that exactly lines up with fill valve.)  This makes the pressure numbers easy to find, AND really help me in troubleshooting a leaky inner tube.  I can inflate the leaky tube in a bucket of water, find the leak, then remove it to line it up with both the rim AND the tire to search out root causes for the leak. 

Edit..
I'm guessing that with certain rim cross sections and geometry, and with a soft rim tape, it might be possible for no sharp edges be exposed with tire and tube is off of the rim, but under high tire pressure, the rim tape may move a bit, exposing the inner tube to the sharp side of a drilled spoke access hole, or the end of a long spoke...