If we assume it is an authentic Dickert signature, then we next think about who wants it and why. A collector of longrifles who would love to have anything affordable associated with Jacob Dickert is one sort of customer. An important piece of longrifle history. To that person, it may be worth $500, maybe $1000. Where else are you going to get something Dickert-associated for that kind of money? A working period flintlock mechanism never restored to flint and suitable for restoration work will start at $300 and go on up. One signed by an important maker? More. So why not a signed barrel?
Next is someone who is restoring an original stock believed to be a Dickert. You might be surprised at some of the original longrifles in books that started out as a buttstock with a few parts attached, but no barrel. I can think of 2 offhand and I have no insider information. Now they are presented as complete rifles. A restored Dickert, seems to me, would be in the pricing ballpark of a restored JP Beck, etc. A buttstock, not so much. So for that unique situation, it might be worth even more than I guessed above.
I'm not an active or up to date collector and keep in mind that serious collectors are reluctant to discuss pricing as it is bound to upset a seller or a buyer out there.
Keep in mind that any uncertainty about the signature's authenticity will affect value.