The Radeon R3 Graphics did well within the synthetic Furmark benchmarks.
More of these OpenGL benchmark results between the thirteen graphics processors on Ubuntu 14.04 Linux can be found via 1404185-KH-AMDKABINI28 thanks to the Phoronix Test Suite and OpenBenchmarking.org.
Overall, when running the brand new Ubuntu 14.04 release and using the binary AMD/NVIDIA drivers, the Radeon R3 Graphics (also branded as the Radeon HD 8400 series) its performance was close to that of the discrete Radeon HD 6450. The Radeon HD 6450 PCI-E graphics card still retails for $40~50 USD so considering that a Athlon 5350 APU can be found for about $60 or less, that's a pretty good deal for the GCN-based graphics paired with the four low-power Jaguar cores.
Compared to the NVIDIA hardware and their Linux driver, the Athlon 5350 was competing against most prominently the GeForce GT 220 and generally ahead of the GT 610 and GT 520. Overall, the Radeon R3 potential under Linux with these AM1 APUs is quite respectable given the very low cost. There's also (slower but improving) open-source Linux graphics driver support for these APUs, as covered in other articles such as the Athlon 5350's RadeonSI Gallium3d vs. Catalyst benchmarks. For those interested in the other APUs there is the four-way AM1 comparison. I've also published some Linux OpenCL benchmark results too, plus other Linux tests of this low-power AMD hardware is still forthcoming on Phoronix.