Is walked a pronoun

No, the Word 'walking' is a gerund, the present participle of the verb 'to walk' that functions as a noun or an adjective.

Example:

Jack is walking his dog. (verb)

I bought some new walking shoes. (adjective)

Walking is good exercise (noun)

A pronoun is a Word that takes the place of a noun in a sentence.

Jack is walking his dog. It is a beagle. (the pronoun 'it' takes the place of the noun 'dog' in the second sentence)