I use a spare dist with the gear ground off with my drill to prime the motor. You can run the flush through that way too. Gas in the oil more likely knocked all the buildup inside the pan and block loose, which is clogging the oil screen. I have hooked up engine flush to the oil sender port and spun the dist backwards to push the crud out of the screen too. I had to do that when I picked up an old Rambler. Driving home the oil light came on at 50 mph so I coasted to the shoulder. I drained the murkiness that was passed off as oil and force fed a quart back down the sender port by turning the motor backwards (with the plugs out and my torque wrench) until the whole quart was sucked in. (I grabbed the oil and pipe fittings from an Irlybird hardware that was nearby)
Then I poured 3 quarts of diesel fuel down the valvecover, caught it on the bottom and fed it through again several times (sans the crud in the bottom) until it came out clean. Then I put in the fresh oil and changed the filter and drove it home. I pulled the pan and there wasn't much crud left in there, but I figure it drove 50,000 miles without an oil change before I got it (going by the sticky on the windshield)