For how long would a flu-contaminated parcel be an effective disease vector?
How long should I wait before handling the parcel to avoid contracting the virus?


If you use gloves, or don't touch your face and just wash your hands after opening, you don't have to wait at all.  If you don't use gloves or want to pick your nose, rub your eyes, or fiddle with your beard while opening the package, wait 24 hours if the package is nonporous, and 2 hours if it is not. Generally, whether contaminated or not, don't lick, eat, inhale, or rub your eyes with the package :)  

Influenza and similar respiratory viruses are transmitted by large droplets, aerosols, and fomites. Your package is a fomite, an object that can be contaminated and transmit disease. There is some debate about what mode of transmission is most significant for influenza, but fomites definitely do transmit influenza and similar viruses. In a study of homes and daycare centers with children who had an active influenza infection, 59% of home objects that were tested were positive for influenza. It's reasonably likely that your package was, at least at some point, contaminated.

@LDiago's answer is useful here, but deserves some clarification. The UK National Health Services information cited in that answer comes from this seminal study. I'm not entirely happy with the wording on the NHS website, though. Virus survives on nonporous surfaces for 24-48 hours. Virus is transferred from nonporous surfaces to hands in detectable amounts for 24 hours. If your package is paper, the relevant test is transfer from cloth or paper. Virus survives for 8-12 hours, and is measurably transferred to hands after 15 minutes to 2 hours. In any case, virus transferred to hands from a fomite survives for only 5 minutes.

Infection from fomites, however, requires virus to be transferred from the fomite to (typically) the hand, and then from the hand to respiratory tract epithelium. Inoculation of nasal passageways is sufficient for infection in laboratory conditions. Conjunctival and oral inoculation may also play a role. You can read more about this in Cecil Medicine Ch. 372 and Murray Medical Microbiology Ch 59.