I had a similar style of platform in my old cage. I just cut the fleece to size, making them slightly wider than the platform, so I could wrap the fleece around the sides a bit, then used metal binder clips to secure them to the platforms. It worked great, I never had any issues with my chin pulling up the fleece.
That said, if I were you, I'd consider getting a different cage at some point in the not-so-distant future. It looks like that cage has an awful lot of plastic, which usually doesn't mix so well with chins. It can really harm their digestive tracts if they naw off a jagged piece large enough to get stuck or cut up their insides.
It also looks like they'd be able to chew right out of the bottom of they had a mind to.
If you can't or don't want to get a new cage right away, you could always remove the plastic platforms and tunnels and replace them with wood ledges, perches, and platforms. Then you could cover the whole plastic bottom in fleece, which would hopefully deter your chin from chewing it. Next best thing would be to cover the platforms and plastic bottom in fleece and remove the plastic tunnels.
Can your chin even use those tunnels? It's hard to tell the size from the picture, but they look like they'd be too small for an adult chin, and I'd worry about them getting stuck inside. They're also not safe at all to chew, so if possible, I'd recommend just removing them. If your chin can't get between the levels without the tunnels, you could buy some wood ramps or something to use instead.
