You can choose the same creature as the target for each time the ability triggers, yes.
But each ability will resolve separately. Only the first to resolve will be able to affect the creature, exiling it then returning that card to the battlefield. After moving out of the battlefield, the creature is considered a new game object, not the legal target of the remaining ability still on the stack. So that other ability will fizzle.
Since Flickerwisp enters the battlefield as a creature while you control Panharmonicon, its ability will trigger more than once. However, you choose targets separately for each Flickerwisp ability that goes on the stack this way (C.R. 603.3, 603.3d, 601.2c). These targets can be the same or different. However, if you target the same permanent this way and one Flickerwisp ability exiles that permanent, the other Flickerwisp ability or abilities on the stack will have illegal targets and fail to resolve (C.R. 608.2b). Therefore, in general, targeting the same permanent this way will have little practical effect, if any.
EDIT (Sep. 23): Correctness edit.
EDIT (Apr. 27, 2018): Edited to conform to rule change in Dominaria.
EDIT (Jan. 25, 2019): Added rule citations.
EDIT (Oct. 1, 2019): Corrected rule citations.
You can choose the same creature as the target for each time the ability triggers, yes.
But each ability will resolve separately. Only the first to resolve will be able to affect the creature, exiling it then returning that card to the battlefield. After moving out of the battlefield, the creature is considered a new game object, not the legal target of the remaining ability still on the stack. So that other ability will fizzle.
Even worse, Flickerwisp doesn't return the exiled permanent right away, only with a delayed trigger at the beginning of the next end step. This makes it even clearer that targeting the same permanent twice is normally useless.
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You can choose the same creature as the target for each time the ability triggers, yes.
But each ability will resolve separately. Only the first to resolve will be able to affect the creature, exiling it then returning that card to the battlefield. After moving out of the battlefield, the creature is considered a new game object, not the legal target of the remaining ability still on the stack. So that other ability will fizzle.
EDIT (Sep. 23): Correctness edit.
EDIT (Apr. 27, 2018): Edited to conform to rule change in Dominaria.
EDIT (Jan. 25, 2019): Added rule citations.
EDIT (Oct. 1, 2019): Corrected rule citations.