Flintoff - son of former England captain Andrew - made his maiden senior hundred in 65 balls, combining with skipper Keaton Jennings (156) in a blistering fourth-wicket partnership of 214.
The Lancashire batter had previously made a hundred for the England Lions, a side coached by his father until Andrew Flintoff announced he had stepped down from the role last week.
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After winning the toss and opting to bowl first, Somerset made the breakthrough in the 14th over when Archie Vaughan - son of former England batter Michael - dismissed Matty Hurst for 47.
Vaughan also claimed the scalp of Josh Bohannon (8) and Marcus Harris (26) was bowled by James Theedom before the Red Rose took control.
Opener Jennings was eventually ousted by James Langridge for 156, with Flintoff departing five overs later, caught by Vaughan off the bowling of Migael Pretorius.
Flintoff had hit his first 50 runs off 37 balls, with four fours and two sixes, and took only 28 balls to score his next 50. When he departed, he had struck 10 fours and seven sixes.
Lancashire started the final round round of One-Day Cup group matches in third place in Group A and look well-placed to progress to the knockout stages this weekend after posting a club record List A total.
