Isn't it true that Dragonborn hate dragons because they were dragon's slaves? If so why would Dragonborn want be a paladin and serve a dragon god like Bahamut

I believe that dragons and dragonborn share gods (don't quote me on that), or they could always worship a non-dragon god.  Also paladins don't even need to worship a god, they can worship an ideal or idea. 

5e Dragonborn lore is conflicted and murky.  Prior to 5e, dragonborn being slaves of dragons was a story, but I don't know how universal it was.  Yes if both Metallic and Chromatic dragons created or treated dragonborn as slaves, it would probably be hard pressed for a free being dragonborn to devout themselves to Bahamut or Tiamat.  But the slave race narrative isn't as embedded into the lore as say it is with the Gith and Mind Flayers.  

Fizban's, ironically, treatment of Dragonborn is sketchy.  In race description it simply says the PHB race is available for characters who want dragons somewhere far in their ancestry, and the more specific metallic/chromatic/gem options don't delve deeper.  The beastiary offers "dracgnborn champions" so somewhere in their setting agnostic view the notion of dragonborn devotees of the "dragon gods" is feasible.

At the end of the day whether your dragonborn are contemptuous of dragons or reverential of them, or the question being entirely inconsequential is a worldbuilding question you're free to answer anyway you'd like.  My dragon cosmology is pretty idiosyncratic, but with Dragonborn there are some devotees of Bahamut and Tiamat, but most Dragonborn recognize they have some draconic heritage, but are not beholden to it.

Yeah Dragonborn lore does seem murky thanks though

I suggest you actually read the dragonborn description in the PHB. Because you appear to be guessing things based on partial knowledge that probably comes from different source material (there is no reference to slavery in the 5e dragonborn description). Beyond that, anything is malleable per DM fiat as to how things work in a particular game.

Edit: Additionally, there is nothing in any official lore that requires paladins of any race to follow any particular god.

dragonborn  are INTENDED to worship bahamut 

or at least that’s what Fizbans and the PHB infer. 

It's whatever you want in your story.

In one unending campaign, the Dragonborn Paladin borrowed lore from older editions where Dragonborn were created by transforming a humanoid, and his paladin order (Order of the Dragon d'Or—yes, as in the restaurants) would transform members into Dragonborn. It is unsure if the transformation is a privilege or a punishment because the leader of the order is a Dragonborn but the player is really bad at playing a Paladin and Lawful Good alignment, and for the backstory, his Dragonborn character was cast out for reasons still unknown after all this time.

The Dragonborn being slaves of dragons is a Forgotten Realms (Abeir) thing not an overall DnD thing. Even their they were slaves of the evil dragons, servants of the good. However Abeir was the primordial’s world While Tori’s was the God’s world after the first sundering. So it’s not clear that they would have followed any gods there. On arriving on Tori’s at the start of the spell plague (1385 DR)they are really discovering the gods for the first time so a FR Dragonborn could easily choose to follow Bahamut. With the end of the spell plague and the second sundering Enlil returned to Faerun as a Dragonborn taking them as his special group - this is still sorting itself out at this time in the FRs. That said if your world is not FRs based there is really no lore about this and you are free to do anything you want.

I don't know if it's still being "sorted out" SCAG does a decent write up mentioning Abeir, but keeps the origin before that murky aside from some connection to IO.  I don't see WotC "doing" anything further with this beyond the even vaguer promptings it offers in Fizban's.  I also don't see anything wrong with that either.

Another interesting option on Dragonborn is Mercer's Exandria book where you have the long origins of Dragonborn again muddled in the vastness of time, but more recent history had one dragonborn kind enslaving another dragonborn kind.  The slave rose up and drove out their former masters who now live in a diaspora of reduced means while the former slave dragonborn build a new nation.

You could also mix up dragonkind even broader, without even necessarily using Fizban's.  I think it was an article in MCDM's arcadia that got me thinking of Dragons, Hydras, Wyverns, the various cute little dragons, and Dragonborn, Lizardfolk, Kobolds, Tortles (because of Dragon Turtles) all stemming from (or technically inspired "life breathed into") a common origin point.  My own dragon mythos leans into that notion.  These Dragonkind live is a sort of diasporic condition.  None of them have great nations, living in enclaves at best, more often solitude outside of short term mating and young rearing arrangements.  Sure some from these backgrounds take oaths or pacts or serve divinities that "look like" their origins (Bahamut, Tiamat, a cult that reverse something like Godzilla), others find their calling in oaths, values and divinities of the worlds more populous peoples.  This is all another way of saying that being a dragonborn means what you want it to mean.