"Will there be any problem ..."

Yes, there will be!

Flash and EEPROM devices require very little current in standby mode and while reading, but can easily consume some 70 - 80 mA while erasing and writing. If the output impedance of the power supply is not very close to zero, there will be an appreciable drop in the supply voltage that can (and most probably will) result in memory corruption.
It is for this same reason that Flash and EEPROM devices require very good power supply bypassing with something like a 100nF high grade ceramic (X5R, X7R) in parallel with a 10µF tantalum (or, like I do, a 2.2µF X7R ceramic).


Regards,
Rob.