Been servicing cars for 40+ years.
I too can remember seeing flushing oil but never used it.
I've always followed the same procedure.
First step was to get the engine nice & warm, remove the sump plug & oil filter.
Leave to drip into suitable containers (washing up bowl from the kitchen sink was a popular choice) whilst doing the other tasks like plugs & filters.
Just need to keep the bowl pretty close otherwise any wind will blow the dripping oil all over the place.
Always filled the new oil filter with fresh oil before fitting too.
I can see the attraction for these oil extractors these days, especially with the hassle removing undertrays & sump guards on modern cars.