I hope you mean 6:15pm.
If you take the 13:06 Nozomi at Hiroshima, you'll get to Shin-Osaka at 14:35, then you can take the 14:45 Haruka Express to KIX, arriving at 15:34.
For train schedules, go to hyperdia.com.
I agree with the first post, we just did it yesterday. The only difference is we had the JR Pass and the Nozomi line isn't valid on this pass. But there's another shinkansen (bullet train) that is and works just the same way. We left Hiroshima station at 10:50 am, went to Shin-Osaka, had 20 minutes to transfer to the Haruka Express which delivers you into the airport. We were there by 1:40 pm. Kansai seems very efficient and mellow, and Delta had us checked in within minutes, and through security in 10 minutes. If you're there by 3 or 3:30 at the earliest you'll be fine!
Just go to a JR Ticket office and tell them when you want to be at Kansai and from where, and they'll reserve it all for you in advance if you like. And remember, the trains run to the minute on schedule in Japan.
You probably have accommodations in Hiroshima but we really enjoyed ANA Crowne Plaza.