Hope you will find better weather by the beginning of March. Rains and cold coming from the Pacific could make the difference, ending a hot and dry summer, but it is a matter not easy to predict.
4 weeks in the country is really good time, more than enough to visit several places and fish in many rivers.
Welsh colonization cities in Chubut province started in the Atlantic coast, were the welsh settled first, (Puerto Madryn, Rawson, Trelew) entering into the country alongside the Chubut river valley to the Andes (Esquel, Trevelyn). If you are interested in the colonization history try to get in bookstores at Bariloche a copy of some important studies (I guess some of them are written in english/spanish) about the welsh people in argentina.
Salmons in the Traful do not run, because they are the landlocked salmon variety (salmo salar sebago) introduced in the area at the beginning of the XX century. You may find them at Ržo Traful but also (if you are lucky to locate them) at Rio
Carrileufu in Chubut.
Concerning flies, if summer conditions prevail, keep on small flies: mayflies, caddis, stoneflies, in nymphs and dry patterns; terrestrials (ants, beetles) also work fine, In sunny days and windy conditions western attractors like wulffs, madame X, stimulators, chernobyls, size 12 - 14 could make the difference. In big waters, cold weather with rain or wind, try streamers size 6- 10 in brown, olive and black tones.
Have a nice trip !!