Ummmm..... there are only two things required (for a citizen of the US) to establish residency in a state for the purposes of firearms transactions:
1. Presence in a state.
2. Intention to make a home in that state.
It's got nothing to do with driver's licenses, taxes, minimum time in the state, etc. The minute a person steps foot in a state with an intention to make a home in that state, for the purposes of firearms transactions they are a resident of that state. If the person is a legal alien with an immigrant type visa but not a citizen, then 90 consecutive days in that state is required.
27 CFR 478.11:
State of residence. The State in which an individual resides. An individual resides in a State if he or she is present in a State with the intention of making a home in that State. If an individual is on active duty as a member of the Armed Forces, the individual's State of residence is the State in which his or her permanent duty station is located. An alien who is legally in the United States shall be considered to be a resident of a State only if the alien is residing in the State and has resided in the State for a period of at least 90 days prior to the date of sale or delivery of a firearm.
In a private party transaction there is no requirement (in about 48 of the states and no Federal requirement) to prove state residency. The requirement is to not know or suspect
the buyer is not a resident of the same state. If the dude lives in a house in the same town and is a citizen of the US, that pretty much seals it - it doesn't matter if he moved there two hours ago and has a driver's license from Mars.