Translation/Meaning: 棒棒机
Burner is not equivalent to, and not related to, 棒棒机. 


棒棒机 implies the form of the mobile phone – a phone that takes the shape of a cuboid, usually with rounded corners and/or edges.
Burner implies the use case of the mobile phone – a phone quickly disposed (burned) and replaced.


The English equivalent you are looking for is a bar/candybar/slab/block phone. 

For more information, you can refer to this wiki page.