Generally you use sae 30 in the older flatheads but if it's OHV then they recommend that you use a multi-grade oil instead. I know Briggs has totally revamped their recommendations to use 5w30 synthetic, 10w30 but doesn't specify which conventional or synthetic, they also list their 15w50 for the hottest temperatures.
Small engines are fairly robust and you can run pretty much anything in them as long as it's actual motor oil they don't complain. I've been running a mixture of 1qt Pennzoil sae 30 and filling the remaining part and then topping it off with Shell RGT 5w30 but I'm using an older Briggs opposed twin. The sae 30 mostly comes only in qt bottles which are more expensive to buy which is why I use the one and I have the RGT leftover from oil changes. I've tried different oils and for some reason Castrol sae 30 made the engine rap a lil more but with the Pennzoil it runs nice and smooth. I've found these engines can sometimes be picky on which oil you choose.