My baby is 6 months now and before pregnancy my period cycle was 23 days. I had my 1st period on 1 March and as per 23 days cycle haven't had the second one this month and I am breast feeding. so can second period or thereafter cycle be irregular and by how many days?

It is not uncommon for your cycle to be irregular (longer or normal than your normal cycle) during lactation. It is also possible for you next period, following the first one, to skip a couple of months. As with regular periods, every woman is different. You can just stay relaxed and observe a few more cycles. :)