Floor prep to laying luxury vinyl planks over ceramic tile
The best solution is to do it properly; remove the ceramic tiles, patch/level the floor underneath, and then install the vinyl as per manufacturer's instructions.  

If you lay the vinyl over the floor as is, the peaks and valleys from the old glue and grout lines will transfer through the thin vinyl. It likely won`t be significant, but noticeable if a person was looking for it.

Patching the grout lines as is may not allow proper adhesion due to the excess glue.  The patch could come loose, crumbling and/or shifting, and cause a lump in the floor.  The glue and any loose material would need to be removed prior to patching the grout lines.  Depending on the amount of patching required, this may be just as much work as removing the tile.

Side Note:  You mentioned that the vinyl planks you`ve picked are waterproof.  While the planks themselves do not absorb water, the final floor will likely not be waterproof.  If you were to have another flood of the basement, water will seep through the seams in the planks and along the edges.  The floor would have to be removed in order to remove that moisture.