Outback Queensland flooding - will it be gone by June?

Try and get a response from the Ranger in charge at Diamantina Lakes NP for your run south from Boulia/Winton. They will have a very good idea. If you can't access the NP, talk to the NP regional office in Longreach.
Failing that private message Member Bob Y. at Winton

Probably a terrible thing to say, but I am not up to date with what the flooding is like out that way currently
.If anything like the Channel country flooding last year it could easily be a couple of months before it's all open again.We waited in Tbooburra for a month before we could get across to Boulia & the Plenty Highway, but even then we couldn't go via our intended route via Windorah & Bedourie.Had to go up through Longreach & across to Winton. Even when we eventually reached Alice many roads in the Channel country were still closed. EDIT. I would think you would be ok by June/July though.

While major routes generally dry out and reopen by June/July, minor back tracks often require more time to be graded and cleared of debris. Floods in the Diamantina catchment can inundate grazing lands and tracks for months, and councils will not open them if they are boggy to prevent road damage.

Keeping an eye on Queensland road conditions here is helpful too.
https://qldtraffic.qld.gov.au

Thanks everyone. I took the suggestion of emailing the ranger (done via the generic Parks website contact form) and they got back to me within a day or so:

I would say at this stage the roads should be dry and open by winter but the waterholes will still be full so a great time to visit. Feel free to contact me beforehand also if you would like for local conditions closer to your trip.

I'll continue my plannng and hopefully it will all work out!