The Kiteboard is 132x39cm, two 1/4" birch pieces glued together.
I am going to fiberglass the top and bottom and was wondering how thick I should glass it.

I have ordered Resin Research Epoxy and 3.7 oz glass. I was thinking of doing two layers of the glass per side. The board flexes a ton right now and can't imagine that it should be that way. I am trying to build a board that will last and my biggest fear is it snapping. Any input is appreciated.

2 layers should be fine - same number as I put on my board I am building which has a slightly thinner core. Not tested it yet so no idea how strong it will be.

1/2" thick should be more than OK - but if it is flexing as you say - which direction is the wood grain ?
It needs to go tip to tip full length of the board - NOT across the board edge to edge, if this is the case - yes the board will snap easily even with the glass and epoxy added.

The wood grain is going length wise. I am more familiar with wakeboards and they have zero flex. My kiteboard is a really old Slingshot Manta and that also doesn't have any flex. I would say the flex is similar to a snowboard.

The 2 layers of glass will stiffen up the board a bit, but flex in a board does help landing jumps, carving turns and getting through choppy water.
IMO 2 x 1/4" ply bonded together would take a lot to snap.

Another option for even more strength is to bond the 2 sheets with a layer of glass and epoxy between them first.

2 1/4" layers of baltic birch is what I used for a 131x39. Plenty strong and the flex is about right.

If you insist on adding glass, I would try 1 layer on top first. It might add the stiffness you're looking for and you can avoid a hot coat. If it's still not to your liking, slap a layer on the bottom.

Put some concave in the board,and that will stiffen the board up, and you'll go upwind faster. Skip the Glass on the outside, adds alot of wt. A stiff wood board is not necessarily a good thing,
If you are skimming a board with fiberglass use a foam layup.