Is there a biblical basis for Pescetarianism? Pescetarianism is the practice of following a diet that includes fish
  or other seafood, but not the flesh of other animals. (Wikipedia)


Any insights would be really helpful, thanks.

To specify, I'm asking from a Methodist point of view.
There is no real biblical basis for any kind of dietary restrictions on Christians. While pre-Christian Judaism had many dietary restrictions they were essentially all lifted by the events of Acts 10. 


  Then a voice told him, “Get up, Peter. Kill and eat.” “Surely not, Lord!” Peter replied. “I have never eaten anything impure or unclean.” The voice spoke to him a second time, “Do not call anything impure that God has made clean.”


There are references in Acts to commands to "refrain from eating of blood" but nothing else. 

There is also no biblical basis against Christians choosing to impose dietary restrictions on themsselves.  The best biblical example here is the "food sacrificed to idols" passage in 1 Corinthians 8.


  Some people are still so accustomed to idols that when they eat sacrificial food they think of it as having been sacrificed to a god, and since their conscience is weak, it is defiled. But food does not bring us near to God; we are no worse if we do not eat, and no better if we do.


In essence if somebody's conscience requires them to refrain from eating particular foods, that is good and to be respected - though not better than the person whose conscience permits them to partake. I would apply that principle whether the 'refraining' was for moral, health, or economic reasons. 

There is nothing in the Bible that would condemn someone just because they voluntarily adopt a restricted diet. It might be a different matter if there were bad side-effects of that choice, for example if they adopted a very expensive diet and thus put themselves into unsustainable debt; or forced someone else to go to unreasonable trouble to accommodate their dietary choices.