There are many suggestions online and I'm sure you've already seen many of them, but most are either impractical (modifying Chrome paramaters, only to have them reset by an update) or even, in my opinion, too risky (patching and installing the unsupported amdgpu driver).
Fortunately the open-source radeon driver got A LOT better since kernel 4.4 (currently run by elementary OS), so there isn't much else to recommend, except a kernel upgrade. Keep in mind kernel upgrades are usually discouraged, especially when it comes to production environments since they can lead to data loss and unstable, sometimes unresponsive, systems. Still, a newer kernel usually brings improvements
If you're willing to test it, notable improvements to the radeon driver have been made beginning with kernel 4.9.
If you run in any trouble booting a newly installed kernel, you can always reboot and select the older functioning one from the grub menu (press and hold Shift key while booting).
Instructions (run the following commands in Terminal, one line at a time, input your password when prompted; lines beginning with wget are long, make sure to copy them correctly):
mkdir tmp
cd tmp
wget http://kernel.ubuntu.com/~kernel-ppa/mainline/v4.9.25/linux-headers-4.9.25-040925_4.9.25-040925.201704270431_all.deb
wget http://kernel.ubuntu.com/~kernel-ppa/mainline/v4.9.25/linux-headers-4.9.25-040925-generic_4.9.25-040925.201704270431_amd64.deb
wget http://kernel.ubuntu.com/~kernel-ppa/mainline/v4.9.25/linux-image-4.9.25-040925-generic_4.9.25-040925.201704270431_amd64.deb
sudo dpkg -i *.deb
sudo reboot
To see the currently running kernel use uname -r in Terminal.
lspci -nnk | grep -i vga -A3