The loads aren’t going to be particularly high, the big chainrings mean less load than say a MTB SS with a 32t chainring (or a BMX with a micro drive). In fact I’d be surprised if the ‘average’ slightly tubby SS’er doesn’t put higher shock loads on the chain pedalling over rough ground than Hoy manages in the velodrome.
All my SS’s have KMC chains of various descriptions. Avoid SRAM PC-1 or whatever their track/SS chain is called. Resist the temptation to run the widest chain possible, they’re not stronger, just heavier (longer pins, same plates) and the width supposedly works against them allowing the chain to rock slightly on the sprockets causing them to break (and obviously don’t go too narrow or it wont fit).