While most canoe builders, current and past, simply varnish the interior of wood/canvas canoes, Morris stained his canoes with a red-ish/mahogany-ish stain before varnishing.
If you intend to replicate Morris's finish, Denis Kallery devised this recipe for mixing modern stains to approximate the Morris color:
(modern formulation suggested for restoration)
2 parts Minwax Red Mahogany 225
2 parts Minwax Golden Oak 210B
1 part Minwax Special Walnut 224
1 part Minwax Sedona Red 222
Many people, however, do not attempt to match the original stain color, much of which does not survive the weathering a canoe may have suffered, or the varnish stripping that is a usual part of restoration.
Stain applied before oiling will have more effect than stain applied after oiling. Since you are likely to be trying to match color intensity of new wood with old if you stain, some experimentation with scraps would be in order.
Further, if you do intend to oil the interior, consider using tung oil rather than linseed oil. It's somewhat more expensive, but is less likely to discolor or darken over time as linseed oil often does.
Greg