Hesitation during acceleration: Between 10mph to 20mph

My 2010 Tundra Limited CM with 5.7 has had the everything updated to try & fix this constant hesitation while trying to accelerate between 10mph & 20mph. During acceleration Between these speeds, the CEL will flash & the truck will only sputter without backfire. This last about 3 to 4 seconds and then it will accelerate & the CEL turns off. I finally was able to get a D.A.P. Tune on my truck today & the same result. Dustin from D.A.P. said it takes about 200 to 300 miles for the ECU learn curve?? I googled that one and found nothing. I have dropped the gas tank and replaced the pump & the ring seal. New OEM plugs & coil jackets. New thermostat along with multiple sensors. I saved the best til last. I currently have a OEM expensive MAF in my vehicle. When I install the cheaper Amazon MAF sensor, the truck runs without hesitation, however the Christmas tree lights up with CEL, 4/lo & another light which all stay on solid without any flashing. Let me know what you think. I need this fixed. Thanks in advance. 2010 Tundra

 

People will need the codes it is throwing for best advice. Have you used a code reader to see the errors?

 

Code reader will not read the code with the Amazon MAF sensor installed. When the OEM MAF is installed. There are no error codes.