There should be no issues simply downloading all the *.deb packages and installing them for the relevant version of the mysql server. Note that you'd also need to grab the *.deb files for any mysql modules you need at the same time.
Then you just install them directly with dpkg, after first having purged all the installed mysql packages ( apt-get remove --purge mysql* ). Personally however I would not do this, I have never found any significant issue using varying mysql server versions between live and dev machines, and particularly if both are the same version, 5.5, I don't see why you'd experience any significant issues, but if it's actually and critically mandatory to run precisely the same versions, then directly installing the deb files should work fine.
Just make sure to download them and store all the mysql files you'd ever potentially need in a directory somewhere so you have them to install in case the versions you needed go away, or in case you realized you'd forgotten a module or something.
If this is only a dev system, I think personally I'd just install the debs directly to avoid versions changing.
But unless you are absolutely certain some key difference exists between those two debian versions, which probably is not the case, it's probably just some security update or something that has no impact on how mysql server processes sql, I'd just use what is in jesse, and not worry about it.
Sample:
http://mirrors.kernel.org/debian/pool/main/m/mysql-5.5/
There you see versions 47 and 55, for example, of the server, and you'd also grab the 'core' package as well to match. Tnen you'd look for any other modules you might need here:
http://mirrors.kernel.org/debian/pool/main/
keeping in mind that with dpkg, you have to install the dependency first, then the next package, or both together in some cases. However, what I would do first, not last, in your case, is to make sure there actually is a functional difference between the different 5.5 versions before dealing with the potential headaches involved in trying to maintain a server using dpkg deb package installs.
Here's, for example, a list of mysql packages you might need. Note that I just grabbed this off a dev box, this is not intended to be an authoritative list, just an example, but it does show that mysql is used in many different places on a system, and you might run into issues trying to downgrade manually, which is why I'd in general avoid trying this method (for illustration purposes I changed 5.6 to 5.5). The key is to take the absolute minimum package list to download manually the deb files for.
dpkg -l | grep mysql | awk '{print $2}'
libaprutil1-dbd-mysql:i386
libdbd-mysql-perl
libmysqlclient15off
libmysqlclient16
libmysqlclient18:i386
libqt4-sql-mysql:i386
libqt5sql5-mysql:i386
mysql-client-5.5
mysql-client-core-5.5
mysql-common
mysql-server-5.5
mysql-server-core-5.5
php5-mysql
You'd just take the existing mysql install that is working and run that command to see the packages you need to download. As you can see, it's a pain, which is why I'd generally avoid trying to do a development install in this way, I've never hit any sql issues, or return issues using vastly differing mysql versions, so unless your sql queries are using things only found in the specific version, which is very unlikely, you are unlikely to gain much. But this is how you do it in case future searchers land here.
Note that most dev boxes are probably running desktops, and have more mysql dependencies than just the mysql server stuff for web development, and that can lead to issues.
