Is it ok to bend a VIA in a Flex Printed Circuit?
The question does not specify the expected number of flexing cycles across the device lifetime. For applications where the FPC will be flexed just once at installation, such as connections between LCD panel and attached backpack controller board, pretty much anything goes. At worst, infantile death of the FPC if it happens, will be detected in a test run.

Assuming multiple flexing cycles:


The location of the via inherently becomes a weak point. Given that flexing already creates stress on the copper layers, this is a conduction breakage waiting to happen. You will notice that if there ever are vias on FPC, they are found on the parts unlikely to bend.
The copper used must also be the thinnest possible, to minimize risk of fracture. This means 1 ounce copper, or thinner even, if the application can stand it.
(Ref: mention of minimizing trace resistance because of high current, from OP's comments) In general, one tries to avoid high current over thin traces on FPC: Thermal conduction in polyimide is so low that other than radiation off the surface, heat offtake is poor, ergo hot spots and circuit damage. Try using thicker traces on the current carrying tracks, perhaps by putting them as the outermost ones on each side. I would still suggest the lowest copper thickness available. A fractured trace won't even carry as much current as thin copper will