Are accepted papers going to be plagiarism checked? here's my friend's situation, he submitted a journal paper then gave up after some time and thought it's going to be rejected after a few rejections in an open access journal,he put some parts (as it is), in a conference paper and submitted this work, to his surprise he got acceptance in both.

I asked him to cancel his conference submission not to risk a potential problem with his open access journal submission. He didn't take this seriously and moved on with both.

what are the chances of him getting caught in this situation, given that it's just about 8 months before he will graduate?
In most of the open access journals, it takes less time to put the article online (one of the pros for choosing open access). It might take less than one month, even some cases, after paying the article processing charge, the journal put the author submitted version online. 

Now, for the conference paper, I guess the time difference between the acceptance date and actual conference date is not more than six months. In several cases, the author needs to upload the final camera ready version to the conference submission system in advance. If the conference maintains a good ethics, then the paper will be automatically verified with similarly checking softwares before sending the papers to the proceedings publication department — during this period, the open access article will be online. 

You get the idea on the consequences.