As stated, it varies by route, date and even day of week and time of day ... QF has sophisticated yield management software which is effective in predicting demand. 3 J seats is 10% of the cabin on some planes. Now if you wanted SYD-MEL J then I;ve seen 6 awards available (and there are only 12 J seats on 738s). Presuming you are looking for LAX/SIN/LHR then pretty much 2 is the limit. Routes like HKG and NRT will have more availability on some days.
Also Platinum isn't a very high status on QF, I have been on planes with 100 Platinums, so you have a lot of upgrade and even award competition on those routes.