Most likely, the same bashing damage as normal bullets do
As @Tritium21 mentioned, Rules-As-Written, firearms cause bashing damage to vampires, or lethal if you hit in the head.
Doing it otherwise will break the immersion
RAI, you fight cool guys (the vampires, the Jedi, etc.) in melee or with supernatural powers, firearms are for weak enemies -- it is a very common trope. If such an easy way to fight vampires existed, every vampire hunter (or at least most of them) would abuse it, just like almost all of lupine hunters have silver bullets in their arsenal -- keeping in mind that to get incendiary ammo you need the right contacts, while silver bullets would need to be crafted for one single purpose.
However, obtaining any of them during the game would require a lot of effort unless your character has very specific contacts, or a very good explanation.
Incendiary ammo doesn't really have any special effect on humans
...so it shouldn't on vampires, because fire burns them same as it does burn mortals.
A quote from a russian book by Kubitsky says that no differences were found between normal bullets and incendiary when firing from distances of 150 meteres and less (they didn't try for bigger distances). Incendiary ammunition is designed to pierce armour (like 10 cm of it) and then burn: rounds simply don't have enough time in the body to ignite properly, even pistol rounds.
After shooting the same targets obscured by a hard barrier, they managed to make the bullet ignite... And got simple signs typical for a point-blank wound. The edges were burnt a bit. As vampiric flesh is very resilient, it could happen that the round shatters on impact, for example, if the whole bullet damage is successfully soaked.
However, speaking about phosphorous bullets specifically, it mentions 3d to 4th degree burns. Phosphorous is not something to be joked about. They even say that smoke can go out of the wound for several days. RAW, difficulty to soak the fire is 9 (chemical fire), the amount of damage is most likely one per turn of burning (part of body exposed).
However, that's about incendiary ammo. What about tracers?
It's a bullet with something that burns brightly when ignited, not something that burns hot. They can ignite something that is easily ignited, read this, for example: a huge fire was started by tracers. But they are not designed for this. The heat is pretty much like that of a candle.
Contrary to incendiary ammunition, which also tends to have some armour-piercing capabilities, tracer rounds shatter on impact with pretty much everything. I have read one WW2 veteran's book, or story, where he remembers to be hit by an MG-42 tracer in his helmet. He didn't take any damage. Some book on forensic pathology, however, claims that damage done to humans by tracers at close range doesn't differ from damage of a normal bullet. The book (by Gromov) comes from 1970, so it probably describes the effect of WW2 tracers -- you may keep it in mind if your chronicle takes place during that time.
Nowadays tracers will probably follow this rule. The author of the article also notes that the wound gets soot-like edging, but it happens due to chemicals involved, and only takes place like a day after the trauma.
However, if speaking about incendiary ammo, the same book says that if it meets a bone on it's path, it shatters and can burn tissue. As vampire flesh is generally a lot more resilient, it may shatter on impact with his body, burning his outside (a bit), especially if the didn't penetrate (deal any significant damage). In this case it is like 1 level (or even die) of fire damage (a part of body exposed) and the difficulty to soak would not be very high.
What would probably happen is Rotschreck
When a tracer impacts and shatters, especially if it catches something flammable, or happens right near the vampire, it may look scary for him.