I have a Fire Genasi Fighter that gets two racial spells, produce flame and burning hands. Both of these spells appear on the spell page under a racial traits section called reach to the blaze. The issue I have is that the burning hands spell requires affected creatures to make a dex saving throw, but the DC isn't listed on the spell like it would be for a character with a caster class.

you can calculate it yourself. I had to for my Genasi Monk. 

Spell save DC = 8 + your proficiency bonus + your Constitution modifier 

Spell attack modifier = your proficiency bonus + your Constitution modifier

Hope this helps! Might run it by you DM too so they can confirm or make a ruling on the matter.

Yeah, I went ahead and added a note on my character info about how to calculate it, but feel it should show on the spell itself like it does for normal spells.

Absolutely agree! 

what would it be for a water genasi fighter?

Its the same for a Water Genasi (assuming you are using the one from the Elemental Evil booklet)
Spell save DC = 8 + your proficiency bonus + your Constitution modifier
Spell attack modifier = your proficiency bonus + your Constitution modifier

For a Water Genasi from Monsters of the Multiverse its based on whatever attribute you selected (Charisma, Intelligence or Constitution)