Unfortunately, there's no Hess gas station within walking distance to BLT. The closest would be the one by Boardwalk, and that's several miles away. The roads in between are multi-lane highways with no sidewalks.
Your best bet would be a cab, probably $10-ish each way.
Or, you could walk to MK, get a bus to the Boardwalk, and walk to the Hess station from there. Still a long trip, with a long walk, in hot and humid June.