I would say the Flood would win.
As a fungal infection they require a single spore to trigger a massive outbreak, and can stay dormant for millenia.
They double up (or more) their forces in any successful combat, taking all dead as resources for new troops.
They retain a similar structure to the races they consume, allowing them to utilise the tools, vehicles and weaponry of those races.
They also harvest the minds of the fallen, scanning through all of their memories to gain vital information against the opponent.
They form a gravemind system which is able to use the mindpower of numerous fallen enemies to telepathically control each flood unit from a distance simultaneously, allowing for numerous strategic operations at the same time, utlising the information gained from their fallen enemies.
They're capable of interacting with Artificial Intelligence, corrupting it to it's own uses, with notable examples being Medicant Bias (which led to the fall of the Forerunners, an advanced galactic wide species), Penitant Tangent (an Monitor of Installation 05) and even Cortana (an advanced human Smart AI, who managed to resist due to her short period of capture, but would have eventually given way and given away details regarding Humanity).
They can form their own humanoid and bigger units without the need for a host body, given an adequate level of biomass, allowing for Pure Flood Forms to exist, including the large behemoth "tank" units, ranged units, and rapid scout units, all of which can transform into one another, with the tank form being capable of producing further Flood Infection Forms.
A Flood unit which is killed, but retains a mostly intact body, can be 'resurrected' by the introduction of an additional Flood Infection form.
The Flood Infection form is a rapid moving and small unit, which can be about a foot tall, and can jump at enemy units and burrow into their body (and maneuvre around armour) in order to find the spinal cord and cause infection and control of the host.
The Flood Infection form can be produced by Carrier Forms, a large but slow battlefield unit which approaches and explodes near enemies, causing damage and spreading Infection forms.
The Infection form can be produced from Pure Tank forms in the battlefield, to aid in combat.
The Infection form can be produced from the environment in large pods, which grow over a flood infected environment.
A flood infected environment produces a constant wave of flood infection and flood pure forms.
The infected environment is therefore extremely difficult to remove by land, due to it's ability to rapidly produce defensive troops.
The only adequate system for eradicating an infected environment is to use high-intensity plasma beams to burn away the infection. Such an action "glasses" the terrain, destroying all life and making it entirely infertile and incapable of supporting life. When a flood infection takes over an entire planet, only "glassing" the entire planet is an adequate method of removal, but will render the planet entirely unrecoverable by manual means.
The Floods downfall is it's inability to produce technology for itself.
Without the introduction of a technologically advanced species, which has space-faring vessels, it is incapable of leaving a planet to cause further infection.
The Flood also relies on food. Without additional plant/animal life the Flood is incapable of reproducing or sustaining it's population and units.
Fungal spores however can lie dormant for millenia in wait for the presence of food.
Not all species are capable of being infected. The Unggoy (grunt) race was immune to infection, as presumably were Kig-Yar (Jackals), Yanme'e (Drones) and Huragok (Engineer).
Those not infected however are still killed, and it is possible that their biomass is simply absorbed into other forms or the flood environment, rather than being revived whole and used as a troop.
The Flood might lack in ability to spread themselves by their own means, and can be starved, but they're voracious, highly intelligent, adaptable, patient, highly infectious and extremely dangerous.
They have nearly conquered the Milky Way once, but were only defeated on account of an extreme galactic Self Delete tactic (which didn't defeat the Flood personally, but starved them out), and nearly began a major resurgance in the galaxy at a later date (only defeated due to their small numbers at the time and a lucky turn of events allowing them to be trapped).
Even so, the Flood still exist as spores in containment on numerous Halo facilities, and are extragalactic in nature, meaning they could always enter the galaxy again. There is no knowing where they came from or how many galaxies they may already have conquered.
Faced against the Headcrab zombie the Flood would win.
Headcrabs attempting to attach to a Flood infected form would not work. The brain of a Flood unit is almost entirely destroyed when in use (following the retrieval of memories).
The flood do not necessarily maintain the head of an infected form, with them often being destroyed, or greatly disfigured, or even being internalised. Therefore a Headcrab is unlikely to be able to attach to a head.
The Flood do not exist entirely in the form of humanoids, with pure forms lacking any actual brain and having no humanoid head, graveminds being too large and infection forms being small and weak (The fangs of a headcrab would likely pop an infection form, rendering it useless) and lacking a head.
The Headcrab itself however could easily be infected by the flood due to it's fungal nature.
Headcrab zombies could further be infected and controlled, as the brain is not required, and infection forms can infect at any point on the body, aiming to then control the spinal cord.
Headcrab zombies are slow moving enemies with a weak head that use melee attacks.
The Fast Zombie is simply a faster slightly more agile version (but not as agile as Pure Forms or even some Infected Forms).
The Poison Zombie is an equally slow enemy whose only ability is it carrying poisonous headcrabs. Headcrabs as described above are useless against the Flood, and it is likely that poison would do no harm to a Flood form.
The Flood forces often have powerful melee attacks (as in Infected forms and Pure Tank forms), have explosive powers (as in Carrier forms) and have ranged attacks (as in Pure Ranged forms), as well as utlising the tools, weapons and vehicles of other species, particularly ranged weaponry, both conventional and energy, which could easily destroy the body of any Zombie or Headcrab, and destroy the Headcrab on a zombie and cauterize the zombies.
Against the Xenomorphs the fight would come down to actual combat.
Flood forms have numerous weaponry and vehicles, as well as a fairly effective maneuverability in many forms, including the ability to climb vertical surfaces and cling o walls and ceilings (stalker/ranged pure form), and can jump great heights and run at speed.
The xenomorph is a fast mover and has effective melee abilities, and it's blood would harm Flood forms.
However I believe the superior fire power and resilience of the Flood (who feel no pain) would just put them ahead.
Furthermore, the Xenomorph can not utilise the Flood as a source of reproduction, on account of the characteristics discussed above.
Flood forms lack a working head and often face and internal organs, so facehuggers would not work.
Even if they could, the infectious nature of the Flood would likely kill the baby xenomorph, or would result in some unusual xenomorph/Flood hybrid, ultimately controlled by the Flood.
The Flood could easily utlise the Xenomorph as a food source. Infections by flood spores would guarantee a successful infection.
Infection forms might have difficulty due to the way in which they pierce into the body, which would subject them to the acidic blood, but may be able to survive to reach the spinal cord.
Ultimately the Flood would out-consume the Xenomorphs.
I can't speak much for the Zerg, Tyranids, Necromorph or The Thing, but based on the above, I would still wager that the Flood would be best able to defeat them in combat, or consume them.
