Gilbert, ‘se parler ‘ is intransitive - it does not take a direct object. The reflexive pronoun is always the indirect object pronoun and hence no agreement occurs. 

See links - in particular the explanation on Laura Lawless site : 

https://www.wordreference.com/fren/se%20parler

 https://www.lawlessfrench.com/grammar/agreement-with-pronominal-verbs/

@ Maarten

Then why in few dictionaries and in few websites which I had referred, they are showing the conjugation with past participle agreement.

check few example sentences here showing agreement: 

Elles ne se sont pas parlées depuis la guerre.

sourece : https://context.reverso.net/translation/french-english/elles+se+sont+parl%C3%A9es

Bonjour Gilbert,

Unfortunately, we are not able to rely on some translation services  --  they do not always get the grammar correct.

Martin is correct  --  the verb parler requires a preposition to complete its meaning and therefore the reflexive pronoun will always be representing an indirect object.

Hope this helps.

Bonne journée

Jim