Flash memory or FeRAM?
Many GBA repros (and later releases of official games) took what was once SRAM saves (needing a battery) and used FeRAM (same protocols as SRAM, more expensive though) with no need of a battery.
I am sure some GBA repros also converted to flash -- converting save formats was commonly done for emulators, flash carts and more up until actually rather recently as these thing go, for flash carts it usually was to SRAM versions matching what the flash cart used but in principle you could go to Flash via the same means and stick that on a repro.
We tend not to see that many GB/GBC repros around here to say. GB/GBC games also use memory bank controllers/mbcs to handle saves which is a bit more complicated than GBA stuff that is comparatively simple (search ROM for save type, simple patch in different location depending upon save type sub type).
Also presuming that you want to lose dependence upon a battery then the battery need not only be for SRAM saves and instead be for a clock (as in day or night) as the GB/GBC hardware does not have one onboard and thus the cartridges themselves need to carry one if they want one (and a means to power it)
http://bgb.bircd.org/pandocs.htm#mbc3max2mbyteromandor32kbyteramandtimer
I have also never seen anybody move to replace their SRAM chips with some kind of compatible setup and GB/GBC hacking is pretty advanced in that direction -- see the things done for the standard homebrew flash cart, if someone could swap out the save chip with one not needing a battery then it would probably have been done and most repro makers are not particularly more advanced here (instead feeding off what others do).