The chains have no speed
Abilities do only what they say they do
In 5e, spells and abilities do only what they say they do. If the ability gave the chains a speed, it would have said so in the line detailing the chains' statistics.
Each animated chain is an object with AC 20, 20 hit points, resistance to piercing damage, and immunity to psychic and thunder damage.
Not only does the ability not give the chains a speed, but the chains are also explicitly defined as objects. An object does not have a speed unless an effect of ability explicitly gives one to it.
Compare to animate objects
For example, compare the wording of this ability to the spell animate objects:
An animated object is a construct with [list of statistics]. Its speed is 30 feet; if the object lacks legs or other appendages it can use for locomotion, it instead has a flying speed of 30 feet and can hover. If the object is securely attached to a surface or a larger object, such as a chain bolted to a wall, its speed is 0.
Notice even an intelligent construct, a creature, (which the chains are not) is required to specifically have a speed given to them.
The ability is lacking much more information than just the numerical speed
Not only does the ability not list a speed but it also lacks a description of how the chain would move (crawling? flying?) and how they would decide where to go. Remember, these chains do not have any form of intelligence or any kind of sight. So, how could the chains have the capability to even decide where to move?
Also note that the Chain Devil is not granted the ability to command the chains to do anything except attack and grapple (which aren't even commands so much as automatic things that happen under the listed conditions). Even if the Chain Devil tried to command them, the chains have no ears or any capacity to understand speech.
The chains are simply objects that are able to make attacks and grapple when the Chain Devil meets the listed conditions. There is no reason to assume that the intent was to give them a speed and, in fact, the lack of key information needed for this to be possible is a decent indicator that this was not the intent. Thus, the chains have no speed.
Note: Having no speed and having 0 speed are mechanically different. Something with no speed cannot move unless something gives it a speed. Something with 0 speed could move once the 0 speed condition is alleviated or if they are able to get a bonus to speed that would increase it above 0. (thanks @DavidCoffron)