Rashi DH b'Bikurim writes that the Matzah Bikurim refers to a Kohen who was given wheat from Bikurim. So we are not discussing left-over flour. (I would suggest that if one leaves flour over from Chanukah to Pesach this is liable to develop worms and bugs and there will be a Kashrus problem involved in eating the Matzos baked from it. In addition it would not be common to make Matzos from the flour at Chanukah time because they would not be fresh by the time Pesach arrives).

I am not aware of a Halachah that the Kohanim must eat Bikurim immediately when they are brought to Jerusalem. Therefore the answer to your question appears to be that the Kohen received Bikurim wheat any time before Chanukah and then baked them shortly before Pesach. If not for the verse that teaches that Matzah on Pesach has to be something which can be eaten in "all your dwelling places" it would have been possible to be Yotzei the Mitzvah of Matzah with these Bikurim.

KOL TUV

Dovid Bloom