Flashing SPI flash using DediProg while having intersection with other device
Yes, there could be problems when unpowered chip sits on the same bus.
IO pins usually have protection diodes to supply voltage, so the unpowered chip can try to load the SPI bus down as it tries to power up via the current it draws from the SPI pins.
Also in general having voltages on IO pins while a chip is unpowered is not normal and if the voltages or current exceed rated safe limits there can be permanent damage.
If the 3V3AUX power is off, the flashing will not work.