Thermal conductivity depends on a complexity of factors, which are really different mechanisms by which heat can be transferred through the body. So we cannot really generalise to say whether fluids have lower conductivity than solids, though in most cases they do. The higher T is the more phonons are present and so the better the conductivity.
Liquid conductivity depends on the mobility of the molecules and their speed.
The higher T is the faster the molecules move. Some solid ceramics and polymers can have very low conductivity, probably because they are made up of very tiny grains compacted together. Heat would not be easily transferred through boundaries between grains. It depends which types of solid you are talking about. But if you are comparing the thermal conductivity of fluid with metal, then it is definitely lower.