I'd not bother with an engine flush, but when changing from dino to synthetic, change the oil filter (only, with top up of oil) at about 1000 miles after swtiching. It will probably be full by then, with sludge and varnish released from the engine internals. After that extra filter change, change at 6000 or so intervals with filter change.

On a worn engine, ecesssive leakage is also possible from worn seals "protected" from lots of oil moving past them by crud, but it's likely you will not have this problem on a well maintained engine.

If you already have oil leaks or consumption problems, they may get better or worse, depending on source. If you have excessive blowby from crappy rings stuck with crud, the synthetic may free them up an cure the problem, or it may just "pump" worse. Some seal leakage may be cured by the synthetic as it contains a softner/sweller additive to counteract the shrinkage effect on old, dino oil soaked seals.

The seal shrinkage problem was discovered in the 70's when Mobil (and Amsoil) first started marketing synthetic oils. The seals absorbed the dino oil, swelled, and wore to fit, so to speak. The synthetic "unswelled" the seals, and they leaked. Old history.

My take is that I won't bother with synthetic on an engine that uses more than a quart in 1500 miles as it costs too much, nor do I sue it in an engine that has front or rear seal leaks for the same reason. Otherwise, just change the oil filter an extra time and you will be fine.

Peter

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1972 220D ?? miles
1988 300E 200,012
1987 300D Turbo killed 9/25/07, 275,000 miles
1985 Volvo 740 GLE Turobodiesel 218,000
1972 280 SE 4.5 165, 000 - It runs!