According to Judaism, what is an acceptable gift to bring to shiva? Are flowers and or food appropriate?

It is considered a mitzvah of the highest order to bring comfort to the bereaved.  In the short Talmudic passage read during the morning blessings each day (Known commonly as Elu D'varim) the list of those deeds for which the reward is eternal in the world to come includes "L'vayat ha meit" which literally means attending to the dead, but is often translated and interpreted as a command to comfort those in mourning.

Therefore the only thing one is required to bring is oneself.  This is especially important in smaller Jewish communities when the family of the deceased wishes to conduct a minyan in their home (10 adult Jews are required for a proper minyan).  Even in larger communities this is important since there is never a guarantee that 10 others will be there.

That said, it is also the proper role of comforters to bring food to the house of a mourner, so that the mourner can focus on the task of mourning and to make sure that the mourner is not skipping out on his or her basic needs.  Generally flowers are not a part of the Jewish funeral ritual.  Among many reasons a particular reason is that we do not add death (cut flowers are technically dead) to a period of mourning.

Ultimately it is best to simply bring yourself and a bit of food that is respectful of the way the family observes kashrut.  If in doubt go with kosher food.