What time of year Henry?
Summer overnight walking in the Flinders Ranges National Parks is not allowed.
And outside of the parks could be life threatening due to heat and lack of water.
We do overnight walks in the Flinders mostly during winter, but a late autumn or mid spring walk is generally fine.
mike is right about Mambray Creek - it has good options for loop walks.
I have done a late Oct overnighter - camped on the Battery [14.7km] and came back via Alligator Gorge and Hidden Gorge [21.8km] for a 38km loop.
See
http://bushwalk.com/forum/viewtopic.php?f=9&t=1345You could break it into 3 days easily enough - or do it over 2 days and camp at Mambray Creek for a night and do Mt Cavan the next day. [11.2km]
http://bushwalk.com/forum/viewtopic.php?f=49&t=18689&p=249313&hilit=climbed+Mt+Cavan#p249313But check out the National Parks pamphlets for other options.
Some have worked out overnight loop walks at Telowie Gorge - you should be able to search for trip reports on this site.
As the Flinders Ranges are a north south linear affair, it is normal for us to use 2 cars and do a through walk along the range.
However, if you are prepared for real wilderness, there are some great loops possible in the Gammons.
See
http://bushwalk.com/forum/viewtopic.php?f=9&t=4370I have also done a loop walk off Parachilna Gorge via Blinman pools and Mt Falkland. See
http://bushwalk.com/forum/viewtopic.php?f=9&t=7740I would suggest some serious research if you are going into these northern parts of the range though.
There will be very few tracks.