Either is or are is acceptable.
Whether to use is or are may depend on:
1 What your teacher says is correct;
2 What style guide you use says is correct;
3 What you think sounds better;
4 Whether you consider "one or more items" to be a singular unit, as in "Seventeen items is all I can afford."
5 Flip a coin.
In this context, it is easy to see one or more items as a singular set:
One or more items in your order is not available.
Some may prefer the rule of proximity, which says to use the nearest noun:
One of more items in your order are not available.
Frankly, the above grates on me, because of the strength of the word one. Or as the Cambridge Guide to English Usage remarks:
For most writers the choice depends on whether you’re thinking of a single case or general principle. Usage commentators in the UK and the US have been inclined to say it should be plural; and the Harper–Heritage usage panel voted heavily in its favor (78%). Yet Webster’s English Usage (1989) found ample American evidence for the singular construction, and it’s just as common as the plural in British data from the BNC. Writers using the singular take their cue from one, whereas the plural-users are responding to those [people] or the [things]. [my emphasis]
The Chicago Manual of Style Online does not have a specific entry that I can find. But in the text of Section 3.21, there is:
If one or more full sentences follow it.., thus: obviously plural.
There is also a question at English Language & Usage:
Which is correct: “one or more is” or “one or more are”?
which has more than one opinion.