To my knowledge there is no such permission you can use for translating blocks. Any user who has permission to administer blocks, will also have access to the "translate" link that is typically used to translate blocks in other language. However there are 2 possible work arounds you may want to consider, as further detailed below ...
Option 1: using the Rules module
But, the paths of such block translation links, typically include the language code (fr, nl, es, etc) as part of their paths. With that, you should be able to get it to work (or at least have some type of work around) by using the Rules module, using a variation of what is described in my answer to the question "How to make the permissions of a module more granular?".
You could start from the very same Rule (in export format) in that answer, and tune it to fit your exact needs. If you have a lot of such blocks, then probably the toughest part would be to tune the regular expression so that it matches the URLs of your blocks for which you want to restrict access. If you only have a few blocks you want to restrict access to, you shouldn't need the Rules Condition with the regular expression. Tuning the roles to be checked, and or the Rules Action should be straight forward.
Option 2: using the BEAN module
You could use the Bean module for this. Here is a quote about its project page:
Think of a Bean as a method to provide new types (compared to node this would be a content type) which then provides an add content interface to create as many blocks as you require (see screenshot below). The bean content can then be placed around the site just like any other block.
Here are the steps you'd have to complete:
- Create 1 Block Type for each of your languages, say
- Create 1 Block for each of those Block Types, say
- Adapt the Block Visibility settings for each of those 3 blocks (using the Languages tab), so that they are only shown in the language they correspond to. E.g. for block
MyFrBlock you only show it for language
- Grant the appropriate Bean permissions (= which roles can perform which operations for which Block Types, aka language with the above Block Types configured).
With that in place, it appears to me that you would have a possible solution. Actually from then on your remaining todo is a variation of the question about "How to limit block management by role?". Refer to my answer to that question for more details about this great module (which by the way has been moved to core in D8 ...).
The video tutorial Drupal Bean module tutorial - using Bean Admin UI provides a great introduction to really understand the power of this module, and the kind of things you can do with it (by only using site building techniques, no custom coding involved). It also shows how the Bean module transforms Drupal blocks into fieldable entities.