Is a Roman Catholic ever permitted to take the Anglican Eucharist? According to the Catholic catechisms or canon law, is it ever canonically acceptable or lawful for a Roman Catholic to take of the Anglican communion?
No.

Canon 844 says:


  Catholic ministers administer the sacraments licitly to Catholic members of the Christian faithful alone, who likewise receive them licitly from Catholic ministers alone.


So Catholics may receive sacraments licitly from Catholic ministers alone.

There are exceptions. In the case of Communion  


  Whenever necessity requires it or true spiritual advantage suggests it, and provided that danger of error or of indifferentism is avoided, the Christian faithful for whom it is physically or morally impossible to approach a Catholic minister are permitted to receive the sacraments of penance, Eucharist, and anointing of the sick from non-Catholic ministers in whose Churches these sacraments are valid.


This applies where it is physically or morally impossible to approach a Catholic minister, and only to ministers in Churches where the sacraments are valid.  Anglican Communion is not valid, because the Anglican priesthood is not valid. Therefore this exception does not apply.  

There is a little wiggle room here, in that if the Anglican Holy Communion is not a valid sacrament at all, then the question of whether it is licit or illicit to take it  (i.e. physically eat the bread and drink the wine) seems not to arise.

However, the Catechism, paragraph 1400, also deals with Catholics taking Communion in Protestant Churches and says:


  Ecclesial communities derived from the Reformation and separated from the Catholic Church, "have not preserved the proper reality of the Eucharistic mystery in its fullness, especially because of the absence of the sacrament of Holy Orders." It is for this reason that, for the Catholic Church, Eucharistic intercommunion with these communities is not possible. However these ecclesial communities, "when they commemorate the Lord's death and resurrection in the Holy Supper . . . profess that it signifies life in communion with Christ and await his coming in glory