I have a trust established in one state.

I have a second home in  another state.
I want to have some NFA assets.

Is there any issue filing, say a form1, with a Trust formed (and domiciled) in one state, and applying for the stamp in another?

I'm not an expert, but once you start talking about multiple trusts that are not all in the same state, you need to refer to each states' laws governing their trusts.

If you want to transfer an NFA entity from one trust to another, I'm not sure if there's an easier process than a Form 4 transfer for that if they are all within the same state. At least within such a case, you don't really have to worry about state law governance. But if you are talking interstate trusts, it's a guaranteed Form 4 with all of its bells & whistles ($200 transfer tax, etc.) + any state laws. And read carefully, because it might not be possible to transfer entities into a trust from another state's trust, within certain states.

The F1 has the reflect the state in which the item is made.

If you want to use it in another state you can file the 5320.20 annually with state 2 address. .20s can be good for up to a year.

As long as the item is legal in state 2 it’ll be approved.