Maddy finished with 122 and Flintoff put himself in line for a hundred too, having reached 70 out of 259 for 3 at stumps.
Things had not been as promising when the tourists struggled to 45 for 2 in the face of movement and lively bounce from a useful pace attack.
The England A captain, Michael Vaughan, again won the toss and took first use of the bat, only to end up gloving a ball from Greg Smith to the wicketkeeper, having scored four.
Maddy and Mal Loye then played and missed regularly at Smith and David Townsend, the latter bowling a tight line and being rewarded when the Northamptonshire batsman was adjudged lbw padding up.
Matt Windows joined Maddy in a stand of 72 until a mix-up saw both batsmen stuck at one end - and it was the Gloucestershire man who had to go.
The unfortunate dismissal brought Flintoff to the wicket and he celebrated his call-up to the England World Cup party by quickly imposing himself without taking chances.
The one blemish in Flintoff's innings came when he was dropped by Smith on the long-off boundary for what should have been a routine outfield catch off the spinner Derek Crookes. The ball then rolled over the boundary rope.
Maddy reached his century soon after Flintoff had brought up his 50, and the hundred partnership followed with an off-drive from the Leicestershire opener - his 11th four.
First day of five; England A won toss
ENGLAND A - First Innings
D L Maddy not out 122
*M P Vaughan c Masikazana b Smith 4
M B Loye lbw b Kemp 17
M G N Windows run out 33
A Flintoff not out 70
Extras (lb12, nb1) 13
Total (for 3, 92 overs) 259
Fall: 1-5, 2-45, 3-117.
To bat: V S Solanki, G P Swann, C M W Read, S D Thomas, D A Cosker, S J Harmison.
Bowling: Smith 20-7-31-1; Townsend 23-4-83-0; Kemp 16-3-41-1; Abrahams 13-2-33-0; Crookes 20-5-59-0.
PRESIDENT'S XI: M L Bruyns, C C Bradfield, H H Dippenaar, M van Jaarsveld, F C Brooker, *D N Crookes, J M Kemp S Abrahams, L Masikazana, D H Townsend, G J Smith.
Umpires: D F Becker and R Brooks.