energy storage and flux produced by an inductor The unit of magnetic flux is the Weber and is proportional to L x I or Henrys X Amps. Flux is also proportional to J/I or energy per Amp.
Energy stored in an inductor is given as 1/2 LxIxI. When I ask where is the energy stored in an inductor the answer is given that it is stored in the magnetic flux. 
The energy stored in the flux is LxI but the energy stored in the inductor is 1/2 LxIxI. So my question is where is the rest of the energy stored?
 A: "The unit of magnetic flux is the Weber and is proportional to L x I or Henrys X Amps."
This is pretty much correct. The self inductance, L of a coil (or in general a circuit without an iron core) may be  defined from the equation $$n\Phi=LI$$
in which $n$ is the effective number of turns on the coil, and $\Phi$ is the flux, assumed to pass through all $n$ turns.
So the unit of magnetic flux is indeed the henry ampere (small letters not capitals) or H A (capital letters!)
As you say, the energy stored in the coil is usually written as$$U=\frac{1}{2} L I^2.$$
This can be written, using the top equation, as $$U=\frac{1}{2}n\Phi I.$$
You come close to this when you say that "Flux is also proportional to J/I or energy per Amp.", but the statement in quotes is a rather curious mixture of quantities and units, and of course it suppresses the factor of $\frac{1}{2}.$
It is indeed correct that the units of $\Phi$ may be written as J/A or $\text{J A}^{-1}.$ We can show, in fact, that the units are the same, that is$$\text{Wb = HA = JA}^{-1}.$$
The easiest way to show this requires knowledge of electromagnetic induction and the volt (V). This gives the relationships between units:$$\text{V = Wb s}^{-1} \text{     in which    V = J A}^{-1} \text{s}^{-1}.$$
There is no missing energy! I'd hazard a guess that one cause of confusion is that you're not distinguishing between equations involving quantities (usually italicised) and relationships between units (upright letters in the Système Internationale and capitals when abbreviated to a single letter).
