Tcs light flashes and p0340 code

SOURCE: Mazda 626 'HOLD' light after gear box oil seal was replaced

I have the same problem with my car I think its the torque converter clutch but you should visit a diagonestic machine just to find out

SOURCE: 1998 mazda 626 check engine light flashing

Your vehicle’s computer system has self-testing capability. When the computer senses that there is a problem with one of the components or sensors it stores the correspondent trouble code(s) in its memory and lights up the "Check Engine" or "Service Engine Soon" light to tell you that there is a problem and you need to diagnosed and repaired it. The list of possible codes number in the hundreds. The code itself doesn't tell exactly what component is defective - it only indicates where to look, or what engine parameter is out of normal range. A technician will have to perform further testing to pinpoint cause and the proper repair. When the light starts flashing the computer is telling you to have the vehicle looked at now before other problems happen.

SOURCE: Check engine light intermittently flashing, car jerking.

Could be fuel or electrical related. Since you may not know the history, this may take a while.
Any amount of smoke from exhaust? White, Blue, Black?
Start with most obvious and inexpensive:
1. Fuel filer clogged (replace fuel filter).
2. Could be the ECM (Electronic Control Module). It controls the ignition spark timing.
A few other things... consider other expert solutions...