Does Hidden Blade's "draw 2" effect still resolve if the targeted unit is moved away from the battlefield (e.g., by Flash) before Hidden Blade resolves?

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Hidden Blade still causes the controller of the chosen unit to draw 2 even if that unit is moved off the battlefield (for example, to base) before the spell resolves. The unit simply won't be killed if it is no longer a legal target when Hidden Blade resolves. [359.3.e.5] [359.3.e.6]

If the targeted unit is moved to another location on the board (e.g., to base by Flash) before Hidden Blade resolves, that unit is no longer a legal target for “Kill a unit at a battlefield,” so it is not killed. The separate instruction “Its controller draws 2” still resolves and that player draws two cards. If the targeted object changes to or from a non-board zone before resolution (so it ceases to be the same game object), the kill still cannot affect it, and the draw 2 instruction still resolves. [359.3.e.5] [359.3.e.6] [359.3.e.4]

You play Hidden Blade from Hidden, choosing a unit at a battlefield as its target when the spell is placed on the chain [811.1.d.2] [355.8]. Before Hidden Blade resolves, an opponent reacts with Flash and moves the targeted unit to base. On resolution, the chosen unit is no longer a legal target for the instruction "Kill a unit at a battlefield" because it no longer meets the 'at a battlefield' restriction [359.3.e.5]. The kill instruction cannot affect that unit and is ignored for that target, but the spell's separate instruction "Its controller draws 2" still resolves, so that player draws two cards [359.3.e.6] [355.10.d].

If the targeted unit is moved to a non-board zone (e.g., banished or returned to hand) before resolution, it ceases to be the same game object and is not a legal target; the kill still cannot affect it, and the draw 2 still occurs [359.3.e.4] [359.3.e.5]. If the targeted unit is moved off the battlefield and then later moved back to that same battlefield while Hidden Blade is still on the chain, the original targeting relationship can remain valid if it never changed zones off the board; but if it never stopped being the same object on the board, the spell still remembers it as a chosen target — however if it is not legal at the moment of resolution it won't be killed (see [359.3.e.3] and [359.3.e.5]). If any other instruction of the spell required information about the target (e.g., referencing the killed unit's Might) and that information is no longer available because the unit changed zones, those checks return null and calculations based on them are ignored [359.3.e.12].

When you play Hidden Blade from Hidden you choose a unit at the battlefield where it was hidden as the spell's target per the Hidden restriction [811.1.d.2]. Once Hidden Blade is on the chain it has a targeting relationship with that chosen unit. If the opponent plays Flash in reaction and moves that chosen unit to base (still on the board), the unit no longer meets the targeting restriction "at a battlefield." Per the rules, if a spell's targets are no longer legal when the spell resolves, those targets are unaffected by the spell as it resolves; other parts of the spell still resolve (example: Void Seeker deals no damage if its target was moved to base, but the controller still draws) [359.3.e.5]. Instructions that can't be followed because of illegal targets are ignored, but unrelated instructions still happen [359.3.e.6]. Also, the draw instruction in Hidden Blade does not target the controller — the spell targets the unit but not the controller — so the draw is a separate effect that resolves even if the unit isn't killed [355.10.d]. If the chosen object instead changed to or from a non-board zone (so it ceases to be the same game object), the kill similarly cannot affect it, and other parts of the spell still resolve (the non-board zone change severs the object relation entirely) [359.3.e.4] [359.3.e.5]. Therefore, in the common case of Flash moving the unit to base: the unit is not killed, but its controller still draws 2 cards.