The objective of the mRNA shot for covid-19 is to make the person produce a antibodies that trap the covid-19 when it appears later. I think that for an allergy you want less antibodies, but an mRNA shot gives you more antibodies.
Also, I'm not sure what part of the peanut butter is the more important for the allergy. If it is a protein, perhaps a mRNA shot can make it better/worse, because the mRNA shot make some of your cell produce a protein.
If the allergenic substance in peanut butter is not a protein, I think it would be more difficult to make a mRNA shot that is good/bad.
It is definitely a protein and I don't see much use for mRNA here. Clearly, there's nothing about the produced protein that marks it as safe just because it was produced in the body's own cells, otherwise the vaccine wouldn't generate a response.
So all this would do is introduce a lot of protein directly into serum. If someone was allergic, that would cause a reaction, and if not, it's not clear what it would do. It may not be a good idea for it to suddenly appear in the body without having been exposed through the GI tract.
I think you have this backwards. mRNA vaccines get your body to produce a strong immune response in reaction to the whatever protein the mRNA got your body to produce. Peanut allergies are caused by your body already having an incorrect and very strong immune reaction to something inert.