No, you can't.
While it is possible to extract DNA fragments and other information from insects and other creatures trapped in amber, dinosaurs escape extraction for one very important reason.
The mosquitoes in amber and dinosaurs did not exist at the same time.
The average age of amber is about 25 million years, meaning mosquitoes existed around the Miocene period, a time marked by the rise of the mammals. Hence whatever blood these mosquitoes sucked must have been from mammals of the time period: early versions of bears, beavers, camels, sloths, etc.
Miocene wildlife -- no dinos to be seen.
By the time the Miocene rolled around dinosaurs had already been exciting for about 40 million years. Some amber is even 40 million years old, but even so there is a gap of 20 million years between the existence of mosquitoes and dinosaurs.
While it is possible that a type of mosquitoes and amber already existed, there are no mosquitoes in amber of that age and time-period that we know of.
Secondly there is DNA fragmentation. Even whatever DNA fragments have been found in younger amber have so badly deteriorated over time, it is nigh impossible to tell what creatures they came from.
Hence dino DNA out of mosquito in amber is one of those pseudo-science facts that only Hollywood can make real.