For the Pickles, mix cucumbers, Bar-B-Q Rub and sugar in small bowl. Let stand 30 minutes. Strain cucumbers and place in glass bowl or jar. Stir in vinegar. Cover. Refrigerate until ready to use.
For the Onion Straws, mix flour, salt and pepper in large resealable plastic bag. Add onion rings; toss to coat well. Pour oil into deep fryer, large heavy skillet or saucepan, filling no more than 1/3 full. Heat oil on medium-high heat. Carefully add onion rings to hot oil. Fry 4 to 5 minutes, turning once to brown evenly, until onion rings are golden brown. Drain on paper towels.
For the Sliders, serve brisket slices on slider rolls topped with Barbecue Pickles, Crispy Onion Straws and Stubb’s Bar-B-Q Sauce. (Store any leftover pickles in tightly covered glass container in refrigerator for another use.)