The colloquial meaning of "destiny", "an attitude of resignation in the face of some future event or events which are thought to be inevitable" as SEP's Fatalism puts it, is in fact compatible with "free will". The prototypical example is the myth of Oedipus, who was destined to kill his father and marry his mother, warned of it long in advance, and free to take any action and precaution to prevent it from happening. But trying to make it not happen caused it to happen. Folklore "destiny" only prescribes the (vaguely described) destination, not the path taken to arrive at it.
Philosophers are usually distasteful of this folklore notion because it is hard to justify a mechanism or agent that lets people act freely, but then contrives the circumstances to make some vaguely pre-specified events to happen anyway. So most philosophers that make a case for destiny make it into Destiny, prescribing every event in every detail. Ironically, this stronger claim is easier to defend, and the lines of defence roughly split into logical and theological fatalisms, and causal determinism.
Logical fatalism is usually treated as sophistry/logical puzzle since the time of Aristotle, and the other two require accepting some strong presuppositions. It is quite easy to make a case for Destiny given an omnipotent/omniscient deity for example, that would be theological fatalism. Under causal determinism the future is completely determined by the present (and therefore by the past), so Destiny is reduced to a side effect of causation. In the materialistic version it amounts to "biology is destiny" (replace "biology" with "character", "soul", etc. in other versions): our biological constitution together with external circumstances completely determines our actions, even if to ourselves we appear to act freely.
At one point causal determinism seemed to be strongly supported by physics (especially by classical mechanics), but not anymore. In hindsight, all that empirical evidence ever supported was that the future is only somewhat constrained by the present, not determined by it. And modern physical theories suggest that these constraints are rather loose, leaving plenty of room for "free will". So all available cases for Destiny are based on shaky assumptions.