England's selectors had made provision for Lancashire all-rounder Flintoff, 30, to play in the four-day match against the champion county in his comeback from ankle surgery.
Lancashire were concerned, however, at the prospect of Flintoff playing that match and a county championship fixture against Surrey at the Brit Oval in the space of 10 days.
He began bowling competitively, following a fourth operation on his left ankle, in the pre-season Arabian Cricket Challenge earlier this month and will now step up his rehabilitation in Lancashire's friendly fixtures ahead of their April 16 start.
Meanwhile Darren Gough has given Jimmy Anderson a confidence boost after the young Lancashire bowler's mixed tour of New Zealand.
Gough said: "Unfortunately, when Jimmy hasn't been playing as much with Lancashire as he should have been, he's lacked consistency. Last year he played quite a bit for Lancashire and I thought he improved tremendously."
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