I'll admit I don't even have a chin and just enjoy looking at the pics, but weighing in because I used something like this to make a custom guinea pig cage. Yours looks sturdier but similar construction.

The connectors are usually plastic, and mostly hold the panels in place, but zip ties are almost 100% necessary to keep the cage from falling apart if moved at all. (Maybe you could find a chin safe material? Twine?)

If you omitted the connectors entirely, I'd be worried it wouldn't maintain nice 90° angles... But if you're handy with wood, maybe you could cut custom connectors? They're basically just a circle (but certainly a square could work too?) with a + shape to fit the corners of the grids into.

As for the floor of my cage I used coroplast (corrugated plastic), to make a custom tray. Cut to fit the bottom, with several inches of rise up the side to catch mess. You can take a box cutter & just cut the back side of the coroplast in a straight line, then bend it to make the tray shape. Inside layer of plastic stays intact & reasonably water tight. Duck tape on the back side of the corners where they can't get at it, and fleece blanket + paper bedding on top. I'm not sure how much of that is compatible with chinchillas, but throwing it out there in case you can adapt it so it is.

It looks almost like an interlocking wire cube shelf that has been purposely rolled out of cube shape. That's just my guess.

Here's an example on Amazon https://www.amazon.com/AmazonBasics-Cube-Storage-Shelves-Black/dp/B0735GRJXY/ref=asc\_df\_B0735GRJXY/?tag=hyprod-20&linkCode=df0&hvadid=216574000717&hvpos=&hvnetw=g&hvrand=5733260016745114793&hvpone=&hvptwo=&hvqmt=&hvdev=c&hvdvcmdl=&hvlocint=&hvlocphy=9012160&hvtargid=pla-385181655836&th=1

Any grids that are 14" x 14" in size and have 9 squares across (like in this example) are safe to use. These are standard C&C grids. There's many of them. The AmazonBasics ones are an exact match, and usually the cheapest. They are often even cheaper in department stores though if you can manage to find them.  

The only exception to this is if you are dealing with baby guinea pigs, as they are small enough to just slip right through the grids. In that case, depending on your bedding setup and wall height, you might need to temporarily baby proof the cage by placing cardboard or something similar in between the grids and coroplast, so the babies can't slip out.