The Zerg are likely able to win so long as the Flood don't start snowballing. Zerg physiology is so redundant, they can survive having every limb blown off and walk it off in a few days. And that's just a Zergling.
The only stumbling block the Zerg would really have against the Flood in the early game, is if they can't adapt their broods fast enough to fight off either infection or the various forms the Flood would send at them. And if there's a Keymind involved, well. The Zerg will probably just get whole-sale mind-controlled like what happened with the Overmind that originally governed them. Then the Flood would have a proxy, which is all kinds of horrifying.
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Let's say for this fight the Zerg got the Overmind, and the Flood had the Gravemind. Would this be enough to tip the balance?
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The Overmind would probably be enough to let the Zerg win even if a Gravemind was with the Flood. The Overmind is the strongest Zerg Psionic until Kerrigan is infested, and even though we never see it do anything in combat it still managed to teleport itself and a surrounding hive fleet nearly smack dab onto Aiur and infested it very, very swiftly.
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Alright, then what about a Keymind? The absolute top of the Flood chain?
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Those can make time and space go cry in a corner. It's not really a contest.