The part where he "gets to keep more of it."

$1 in charitable contributions does not lower your tax burden by $1, and certainly not more than $1.

If that dollar would have been taxed as capital gains, assuming 20% capital gains and 3.8% NII tax, it saves 23.8 cents meaning the $1 donation costs 76.2 cents.

If that dollar would have been taxed as normal income, assuming a marginal tax rate of 37%, it saves 37 cents meaning the $1 donation costs 63 cents.

(These two examples are not intended to be an exhaustive list.)

Charitable contributions cost money, just not as much money as they would if there wasn't a tax deduction.

Pay himself with the charities money, as he is an employee of the charity

Why does Bill Gates earn nothing through the Bill and Melinda Gates Foundation?

Lobby politicians using the charity’s money

A 501(c)(3) organization is subject to heightened restrictions on lobbying activities, A 501(c)(3) organization may engage in some lobbying, but too much lobbying activity risks loss of tax-exempt status. Lobbying may not constitute a “substantial part” of the activities of the 501(c)(3) organization. ^[source]

Otherwise direct the charity to work in his best interests

I guess you can argue that eliminating malaria is in his best interests, but it's pretty reaching. I guess nobody should do anything good if it might indirectly benefit themselves.

Issue is if he's paying himself with the charity's money he'd have to pay tax on that, and if he wrote that off with a donation and paid himself again then it'd reset the loop - there's no loophole there, literally, as it'd be an endless closed loop of transferring money.

Given the best interests of the US government are destabilising other countries and supporting unfair healthcare companies, given what is known about Bill Gates' charity spending I think a higher proportion actually goes to the betterment of society than would if it went to the US government