If it were practical to do this, someone, somewhere, would have done it. Instead you have to trade off between flexible armor, and nice solid protective plate that doesn't flex at all.
In the real world everyone seems to have been happy to make that compromise in favor of protection, but obviously you're operating under slightly different constraints. If you want to keep your armor vaguely realistic yet also flexible, then you'll have to dispatch with the idea of nice protective plate and use some other kind of material.
The classic would be chainmail, of course, which whilst it doesn't stretch is quite flexible. There are other options, including metal plates connected by chainmail, or attached to a fabric backing. Here's some nice Han-dynasty lamellar armor using small metal plates:
Or an Ottoman krug using much larger plates linked by chainmail:
You're not limited by material technology or cost, so you can make the non-flexing plates as large as you like.