Ok, you have landed in the JetCat forum, but no matter. White smoke is generally a positive indicator that the flameout was caused by air in the lines. The usual causes of a takeoff flameout are an air leak at the UAT or the feed to the UAT which caused it to drain out, trapped air in the inline filter that found it's way to the engine, or some other air leak.

Check the lines for air bubbles. Often enough, the fill line to the UAT doesn't get completely plugged and it sucks air. Festos in the feed lines to the UAT or even after the UAT will sometimes suck air. I have seen trapped air in the filters take several flights before it clears if the system wasn't purged right. Stationary airplane doesn't vibrate. But it does when it bounces around on the gear during taxi and takeoff which will cause trapped air to purge.

You'll just have to find where. Did you look to see what the ECU reported for the shutdown??

Just a side note, my Rafale flamed out in flight the other day with the usual white smoke. After ripping out all the tanks, I found a stopper on the main feed tank had loosened up enough to suck air. Unfortunately, that tank was buried where I had to take everything out of the front of the airplane to get it out.