The money he is giving away is going to foundations managed by his children (last I read).
Though unlikely the case here, family foundations should always be looked at as a likely source of corruption.
You cannot bribe me directly - that would be caught. However you can donate money to my family foundation and my kids (or spouse) will draw a large salary from it while doing almost nothing and they do some good for the world so it looks like a charity. Of course the kids/spouse will support me in various ways that all rich kids will.
Again, probably not what is happening here, but every time you hear of a family foundation you should ask who they are using it to corruption in some form. Even when it doesn't seem to be you should still look.
That's recent, just as of the last couple months. Historically the children's foundations have been a sideshow and he's given the bulk of his wealth away to the Gates Foundation. You can see that from the dollar amounts: this year's gift to the children's foundations was 1M BRK-B shares (the equivalent of about $500M) to each, while he's given away a total of $66B, over 120x as much.