I'd never even heard of a sinking fund before. Although I do always project that we'll spend an extra $10k per year on unexpected expenses, so I guess that's similar.
How I deal with lumpy expenses is -- um, I don't understand the question. When we have larger expenses, we pay them. I guess we keep a good-sized cash position (5-8%), but in a way, that's irrelevant, because if you always want a certain cash allocation, then if you have a large expense, you ultimately have to replace that cash anyway by selling other assets, to maintain your target AA. But I guess a larger cash position does give you a little flexibility as to timing. (But not market timing, of course.)
We've been FIREd for ~5 years, and we've had some larger lumpy expenses the last couple of years, with more coming soon. I just look at the portfolio, see if we're ahead or behind projections based on an average 7% return (based on our AA), and determine whether we feel flush enough to afford them, or whether we want to postpone for a year or two if possible. But that's mostly for my own peace of mind.
One thing -- to me, "income" means money coming in, from whatever source. "Spending" means money going out. The two aren't always the same, even in retirement. So I got a bit confused by your question at first.