I don't know for sure. It would depend a lot on the exact models in question, fuel loadouts, altitude and initial airspeed.
However: Climb rate comparison typically gives pretty good relative information about acceleration at slow speeds, because it fairly directly corresponds to thrust/weight ratio (although wing loading has some effect on it as well). If you have higher thrust/weight ratio, it means at level flight your engine provides better acceleration.
As a gut feeling I would say at slow speeds the Spitfire accelerates best. The difference between a P-51B/C/D and contemporary Focke-Wulf 190 Anton would be smaller, but I would say it's likely that the P-51 would in most conditions accelerate better.
FW-190 Dora has climb rate that is a close match to most contemporary Spitfires, excluding perhaps the Spitfire Mk.IX with 25 lbs manifold pressure, as well as Griffon engined Spitfires. The D-9 out-accelerates the P-51 at low speeds, and would come very close to the Spitfire's acceleration or better, I think. I have a slight impression that Spitfire (contemporary to a D-9) would still initially accelerate better, starting from low airspeed.
At high speeds, things get different as the planes approach their top speeds. The FW-190 Anton had higher top speed at low to medium altitudes than most contemporary Spitfires (at least until Mark IX), so at high speeds the 190 would accelerate better simply by the virtue that it would be capable of reaching a higher top speed - the Spitfire's acceleration would end at its top speed earlier than the FW-190's. At high altitudes, the Merlin engine of Spitfire would likely outperform the FW-190's BMW engine.
At high speeds, the P-51 would out-accelerate both Spitfire and FW-190 Anton, because it had the highest top speed of these planes. Or, its acceleration would continue longest, however you wish to look at it.
Again, bringing the Dora into the equation mixes things a bit. I would expect it to out-accelerate the Spitfire and 190 Anton easily at high speeds and depending on altitude it might even out-accelerate the Mustang. At high altitudes, the Mustang would accelerate the longest, reaching highest top speed. At low to medium altitudes and high initial speed, the FW-190 D-9 would likely accelerate the best out of these four planes.
Note: None of this is based on any flight performance data or even IL-2 Compare, just my impression and gut feeling about the capabilities of each of these planes.
Dive acceleration would be another thing yet again...
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