I think you only need the recieving DS to be flashed. I've never flashed a DS or used a flashed DS, so you may not want to take my word for it.
As far as running flashme, I've seen people say they've flashed their DS with a G6. The only other thing you would need is a way to boot the G6 in DS mode, and the R4 will do that just fine.
If you plan on having both slot 1 & 2 carts in your DS you may not want to flash it. Flashme will automatically boot the slot 2 cart unless you hold a button (select, I think) while the system boots, ignoring the cart in slot 1. More of an annoyance than a real problem, but you will have to deal with it every time you turn the system on with both carts in it. If you only have one cart in the system at a time it won't make a difference.