It's totally fair to complain about one of the most powerful people in history transferring wealth from public, democratically-elected organizations to institutions that have far less transparency and no democratic oversight.
I fully agree that there is something criticise here, but it's definitely not that he is somehow taking "our" money. It's his money until he decides to spend it. It's money that could be hours, if we instructed our government to take it from him. But we haven't, so that's that.
I like the idea of charitable foundations being able to receive tax free, though I would admit that is a matter of taste and not a clear right/wrong distinction. What I do object to is that his family has paid positions in those foundations. That just smells of tax loopholes. If those foundations manage to perpetually break-even, they would be able to fund his family with cushiony jobs forever.
But, as far as I can tell they're not being paid egregious amounts, and the foundations are all actually spending their money on good things, so in this case there doesn't seem to be any shadowy business. Especially since most of it is going to the Gates Foundation anyway.
But, if we're talking policy, I think it would be a good thing if there were restrictions on how much family members of philanthropes can earn at charity organisations, if anything at all.