The easiest way is to copy your current wallet.dat and replace it on second machine.
So you'll have two copies of the same wallet on both machines.
Always make a backup of your main wallet.dat if you don't dump a private key.
If you just want to start mining on second rig, you don't need to make a wallet.
Make two workers.
here are example for two rigs:
Nvidia EWBF
1) miner --server votecoinmine.site --user your_wallet.rig1 --pass any --port 3333 --eexit 3
2) miner --server votecoinmine.site --user your_wallet.rig2 --pass any --port 3333 --eexit 3AMD Claymore
1) ZECMiner64.exe -zpool stratum+tcp://votecoinmine.site:3333 -zwal your_wallet.rig1 -zpsw any
2) ZECMiner64.exe -zpool stratum+tcp://votecoinmine.site:3333 -zwal your_wallet.rig2 -zpsw anyYou'll see two workers on pool and they will mine for one wallet address, like
this one