According to the latest flat style I feel that attached image shouldn't have a separator to separate comments.
Let me know if it's a good idea to separate comments or what are the latest trends and which will work better?
You just need to ensure the eye can easily find the places where a new comment begins. In your mockup, the images are strong, and (significantly) the comments are SHORT. What happens if the commenter has no image? Or if the comment is longer? Or if the comment (somehow) ends up without a bold heading?
In other words, right now, your mockup is satisfying, but will it survive the real world? Possibly.
There's nothing special about the flat style. You can play around with separators that aren't separators. For example, taking a "nick" out of the left edge, as if cutting a triangle out of the keyline with a pair of scissors. Or using a background on the header line of the comment, etc.
Independently of trends, remember that here the main idea is to improve the transmission of content, so if you can improve that with a single line, a box or a shadow, then that's the best option over flat.
In your case, there seems to be enough space so the comments are clearly identified.
Personally I think that a way to make it more clear is always better, but that is just my opinion.
Over a long comment thread, it might get difficult. Also, if you want to move to even one level of indentation, you will have some problems showing nested comments.
The image attached looks clean to me and is quite readable, however, it depends on your use case scenario. What would these comments be for ? If it is meant to be on a discussion forum, where there will be a lot of conversations happening, I would strongly advise against using this form. I would ask you to make it easier for the eye (I hate myself for saying this - but check out 9gag's commenting system)
If this is a casual forum with not much interaction but a few people leaving their opinion, like on a blog - this would look good.
I can make two points here.
1. Your UI looks incomplete:
Space can be a separator. And looking at the picture, I feel that users will be able to clearly distinguish between the two conversation items. So this approach serves the purpose of the separator. However, most of the users are used to interact with apps which uses a thin line as a separator. Not having a line separator can make the UI look incomplete.
2. Prevent users from accidental click on unintended item:
When you have a line separator, it is quite simple to decide where to click and where NOT to. In this approach, your users will always need to take care of clicking/tapping only on the content section. This is very important in case of touch-screen platforms. If you have a line separator, it can prevent user from accidental taps on unintended items.