I am afraid from the British perspective, this is socially awkward and many people may take offence at being told that. People may not want to share your origins, however impeccable they may be. It is too much of an imposition. In general, it is quite rude to use the term "your origin(s)" with anyone you are talking to. In the UK, we normally use "origins", in the plural. Example: His accent betrays his upper class origins. Another example: In terms of social origins, his father is a stockbroker and his grandfather was a miner. In terms of good English, in general, the correct English is "They come from a similar (social/educational) background." Again, be very careful about saying to anyone, "We come from a similar background." People who are genuinely from the same background recognise one another without having to say it. If you have to say it, you are not from the same background. Neither of your expression is correct English. You need to use "a similar origin" or "similar origins". If you really wanted to, you could say, "We share a similar origin", but it is so much better English to say, "We come from the same background." In terms of the "kind of", I would not use it at all. It is entirely redundant. "Similar" already has "kind of" embedded in it. In general, it is much better etiquette to stick to the facts and not to draw unnecessary overt sociological conclusions. Just say, "We were at school together", "Her mother and mine go to the same church", "His father was at Harvard with mine", "Our fathers were in the same regiment in the army", "She was my prefect at school", "We belonged to the same intake at JP Morgan", "Her brother was at Andover with mine", "Her brother went to Ludgrove with mine", etc.

Americans use "kind of" or "sort of" as a way to say "approximately". It "softens" the meaning of the sentence. Both sentences could be correct but the meanings would be a little different. "Kind of" is placed BEFORE the word it describes. - We kind of share a similar origin. Here, "kind of" describes "share". It means we "approximately" share a similar origin. It may not be a true/real sharing, but it seems or appears (approximates) that way. -We share kind of a similar origin. Here, "kind of" describes "origin". It means we truly share an origin of some kind. Our origins are "kind of" similar means that they are "approximately" similar or just a little bit similar, not very similar. If you ask me if something is accurate, I may answer, "Well, kind of." This means it is "kind of accurate" or "approximately accurate", not very accurate.

I tested your "We share a similar origin" on a native speaker friend. His response was, amusingly, "Do you mean God? Or are you being Darwinian?" You see. It's not quite what you thought, Shirleen.