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I wouldn't try anykind of flush. Get a siphon pump and pump out the rearend. Two bottles of GM Posi-trac additive, and your favorite rearend lube ( I used GM rearend lube.) According to the owners manual the rearend holds 3.7 US pints. (59 oz.) Almost two quarts. On my car I bought two bottles of positrac fluid (4 ozs each) and two quarts of rearend lube. I poured in one bottle of posi-fluid, then one quart of rearend lube. Then the other bottle of posi-fluid and topped it off with the second bottle of rearend lube.
Make sure you go out in an empty parking lot and drive a few tight figure eights, to mix up the posi-fluid and the rearend lube. If you don't a Gawd awful clunking sound will convince you that the rearend is getting ready to fall out!
Good luck.
Hehe...sure, but I wouldn't want to be around when you ask her, or if she finds out! Also, my manuals require only one 4oz bottle of additive, but the 3.7oz is also what my manual says as a full fill level. Buy two quarts (I use Pennzoil 80W-90) and the additive, mix and pour until it begins to bleed out of the filler hole.