You can still scorch wood that has been oiled, but the results are likely to be different to when the wood is bare.
As with almost all finishing you'd ideally want to do some experimentation before committing to doing this on the job, but that's not easy without a piece of scrap wood to do some testing with. You could perhaps use the underside to try this out but only if it's been similarly treated. And note that the time between oiling and doing the scorching might be critical here, as linseed oil is a drying oil it changes chemically over time, polymerising due to a reaction with oxygen.
Caution: if you decide to go ahead, this is probably an unnecessary warning but do yourself a favour and don't attempt to do this indoors. Wood smoke is not a great hazard, but scorching linseed oil could release airborne compounds in the smoke that you don't want to inhale even in limited amounts. Also, linseed oil is quite flammable so the wood could ignite in a way that a big piece of solid wood doesn't generally.
If you don't decide it's worth the risk trying the scorching you can still colour the wood, just using a more conventional method.
A coloured varnish (e.g. "gel stain") can still be applied to oiled wood and the results are controllable and fairly predictable. These sorts of surface coatings are quite transparent, so you will still be able to see the original grain of the wood if you don't go too dark. Some before-and-after pics to illustrate: