something to consider, the fire tablet os is a fork of android. because of this, even though you were able to install the play store and apps from it, they will be unstable and could break whenever there are updates from either google, dashlane, or amazon.
In this case you have an older os that may no longer support dashlane. You may need to find an older version of it to run on your tablet. you can also contact the developer through the play store. Just go to the app in the store and scroll down to developer and contact their support.