This issue was brought up today. A preprinted consent form at a local hospital has latex allergy listed as a contraindication for vaccination.
The vaccine itself seasonal or H1N1 regardless of live attenuated intranasal or the injectable vaccine does not contain any latex.
It is only the top of the bottle on multi-dose vials of the injectable vaccine that does contain latex. This would therefore not recommended in those with latex allergies.
Persons with latex allergies can take single dose vaccines.
Link to package insert