What are my chances to get a hike in the career if I do MBA in logistics through distance?

If you want the required hike in career, I would suggest you to pursue full time MBA from a reputed institute.

There is rarely any chance. A distance learning MBA is helpful for you, if your current organization demands an MBA. For knowledge, it may be beneficial, but you can opt for a distance learning with compulsory weekend lectures or a part time MBA.