Not Medical Advice: You can use Vicks VapoRub if it's just a 'henna tattoo'. Sources suggest that camphor and eucalyptus, both develop stains; making it stick to the skin for a longer time.
As per Buzzfeed.com, you can apply Vicks VapoRub after all the henna has flaked off and keep it overnight. Warming your hands close to a stove or fire helps too.
For permanent tattoos, using petroleum-based products are not advisable. Most of these product types are very dense and heavy. Even applying a thin layer can prevent your tattoo from breathing properly. Not only this but some petroleum-based products contain ingredients that can actually draw ink from your tattoo if used too often.
Check out this ultimate tattoo aftercare instructions guide shared by Authoritytattoo.com.