Should I ask for permission from the journal before making available publicly the (anonymised) text of the evaluation I received from peers?
Unless you signed a very peculiar publication agreement, you are under no obligation to keep the reviews your received confidential.  Moreover, there is probably no issue with copyright infringement either.  Publishing a modest amount of text, for the purpose of critiquing it, almost certainly qualifies as "fair use" of potentially copyrighted material.  (This could, however, vary from jurisdiction to jurisdiction.)

So I think there is rather little legal risk of doing this.  However, it sounds to me like a very poor idea nonetheless.  In most academic contexts, the dangers of doing something wrong come less from formal legal repercussions than from the damage that may be done to your professional reputation.

Presumably everyone who has published in these journals understands the relatively lax nature of their peer review (having gone through the process themselves).  Unless one or more of the journals has an undeservedly high reputation (which seems doubtful, since you describe them as "national"; prestigious journals typically have international contributors and audiences), publishing accusations of laxity against the journal are not likely to affect the journal at all.  On the other hand, doing something like that can definitely get you a reputation as an obnoxious troublemaker, which can be extremely damaging to your career.