76 Plymouth Valiant won't start

The fusible link, is like a slow-blow fuse. The smoke is telling you that it is overloaded. The overload means there is excessive current passing through it.
Since it's only happening during "start mode",(right?), Something in that circuit is pulling a lot of juice. It cannot be the starter, cuz it's on the isolated side of the relay.That's a pretty basic circuit, so it shouldn't be hard to find.I say "shouldn't be", cuz with electrics, there are often surprises.
Dell will be along shortly to walk you through it.But in the meantime, I would check the back of the ballast resister block for a short to ground, as that seems to me, barring a bare or pinched wire, to be the most likely place for a short to occur in that circuit.
But if it also smokes in the "run" position, then there other things to check.
And, of course, the link will have to be replaced.