I would like to know whether I should use "from where" or "from which" in the following sentence:
The bird was standing on the table, from where/from which it flew toward me.
Neither is wrong. The choice is stylistic, not grammatical.
whence would be an archaic alternative, that is similarly being deprecated like whom.
There is no need to use a relative clause at all, because there is no selection to make. If you are merely expressing a sequence of events, then or before can order the events in the temporal domain, so that the tempus can remain constant. In fact, a temporal marker like before is almost required to correlate different tempi.
The bird stood on the table. Then it flew towards me.
The bird was standing on the table, before it flew towards me.
before also has the advantage that it historically relates with front, pre- etc. So it expresses immediacy in the local domain as well, cp. before we go in.