Check the alignment and for loose steering or suspension parts, like tie rods, ball joints, A-arm bushings.
What a lot of folks call "warped rotors" can be something as simple as uneven friction material deposits. Since you had the rotors replaced as well as the pads, there's a proper bedding-in procedure. If they actually did that then they surely would have noticed the shimmy-shake. If they didn't, then it's possible that you could get away with sanding the rotors to remove any friction material deposits, scuff the pads (yeah, you'd have to pop the pads out), and then go do a proper bedding-in per the brake pad manufacturer's instructions.
It could also be that the flattened tire has some damage, but you said it doesn't seem side-dependent, so that's less likely.
If the tire pressure is too low, braking could cause the contact patch to change enough to put the knobby shoulders onto the road more. If they're unevenly worn, they could contribute to the shake.
Inspect the wheel bearings for proper installation by doing the 12-and-6 o'clock check, and the 3-and-9 o'clock check.
All of this is just spit-ballin'. Hope it helps!
What a lot of folks call "warped rotors" can be something as simple as uneven friction material deposits. Since you had the rotors replaced as well as the pads, there's a proper bedding-in procedure. If they actually did that then they surely would have noticed the shimmy-shake. If they didn't, then it's possible that you could get away with sanding the rotors to remove any friction material deposits, scuff the pads (yeah, you'd have to pop the pads out), and then go do a proper bedding-in per the brake pad manufacturer's instructions.
It could also be that the flattened tire has some damage, but you said it doesn't seem side-dependent, so that's less likely.
If the tire pressure is too low, braking could cause the contact patch to change enough to put the knobby shoulders onto the road more. If they're unevenly worn, they could contribute to the shake.
Inspect the wheel bearings for proper installation by doing the 12-and-6 o'clock check, and the 3-and-9 o'clock check.
All of this is just spit-ballin'. Hope it helps!