It's not forbidden, but the closing "etc." is somewhat redundant. The abbreviation e.g. (exempli gratia) means "for example", and etc. (et cetera) means "and other things."
So your text would be: Bring to the picnic what most people snack on, for example, apples, oranges, potato chips, and other things.
Or, to put the same thought another way, when you say eg, it automatically means that there are other things in addition to the examples you are listing.