Apparently, this quote is from Criminal Minds, an American TV series.
Marvin Caul: If you want to lift someone's wallet, don't kiss the dog.
Finn Bailey: What?
Marvin Caul: Don't let him see your face. You almost had it, then you
looked him in the eye and lost your nerve.
Dog can be used to refer to a person, usually informally and offensively. The speaker might say a girl is a dog if they find her unattractive. You might say someone is a dog if you strongly disapprove of them. See definitions 3 and 5.
However, as with many slang words, they can mean the complete opposite. It can be a friendly and casual way to refer to your buddy, to a (usually, male) friend. See my dog.
It can also bear a neutral meaning (just an informal form of addressing a man, boy), which I believe is the case here.
Don't kiss that person.
Don't kiss the man (in question).
Don't interact with them. Don't do anything with/to/around them. Don't make them see/remember/notice you.
The advice is sound - you don't want to kiss a person you are about to steal a wallet from.