Typically your sampled fluid velocity data would 'live' on a specific element of the mesh. For example in 3D, the velocity field 'lives' on the faces of your volume mesh. They are scalar values on faces representing the flux of fluid through that face.
This is a good explanation of how you calculate differential quantities on the discrete mesh.
The flux on a mesh is a 2-form and the gradient of that would be a 3-form, meaning it lives on cells of the mesh. In data it would be 3 numbers stored at the cells representing difference in flux in the x direction, y dir, and z dir. The gradient operator on the mesh is literally a difference flux1-flux2. So your numbers at a cell become [flux(x+)-flux(x-), flux(y+)-flux(y-), flux(z+)-flux(z-)].
I assume you're on a regular cube mesh... If not, then everything is a little different...
This is an implicit representation of gradient of u. Which is a diagonal matrix in the basis representing the orientation of the cell.
Presumably your pressure data also lives on cells of the mesh so you can simply multiply by the identity and add them to your grad(u)+grad(u)T. Your result in data would be a 3x3 matrix at each cell of the mesh.
This is an implicit representation of your stress tensor. I believe the resulting diagonal matrix will represent stresses in the orientation of the cell. The choice of discretizing velocity as fluxes forces your stress matrix to be diagonal. You can rotate the basis of the stress tensor to something else, if needed, then it won't necessarily be diagonal.
If for some reason the data you recorded for velocity doesn't 'live' on faces, that's still ok. You can do an additional step to convert from wherever your data lives to the faces. For example, if you chose to represent velocity data as (x,y,z) vectors at the cells of the mesh, you can integrate the implied velocity field across the faces, resulting in the flux representation of your velocity field. You would need an interpolation scheme to do the integration, like HBR said. But a super simple method could just be to take the difference between the component of your (x,y,z) velocity in the direction of the cell face, with the component of the (x,y,z) velocity on the other side of the cell face. This is clearly not a smooth interpolation though. There's lots of interpolation schemes.