Does Luke 16:25 support Spiritism? Luke 16:25 But Abraham replied, 'Son, remember that in your lifetime you received
  your good things, while Lazarus received bad things, but now he is
  comforted here and you are in agony.


Link to verse in BibleHub

Does it allow us to understand that Spiritism is correct? Your suffering in this life will define what will happen to your soul?

Edit

I'm just curious to understand if there is a relation with your current wealth/poor life and the life after death. This text, in my opinion, is in accordance with the Spiritism, roughly speaking, the way you live your current life will dictate what happens in the next one.
The believe in the existence of Spirit is accepted by many, theist and atheist alike. The Bible also has many verses related to spirits. In spite of all kinds of theories, like the one you mentioned, I will stick to Biblical teaching only.

According to New Testament, the destination/fate of the soul lies solely on the Faith of that person, not his deeds, of course, Faith should be incorporated with deeds. The rich or poor status of the person also does not define the progression of the Spirit as mentioned in the Fundamental Principles of Spiritism.


  John 3:16 (NIV) For God so loved the 
  world that he gave his one and only Son, that whoever believes in him
  shall not perish but have eternal life.


There is no concept of Progression or Rebirth of spirit in the Bible.


  Hebrews 9:27 (NIV) Just as people are destined to die once, and after
  that to face judgment 


In the parablea of The Rich Man and Lazarus, there are things we should know.


Being rich does not make you a sinner. But worldly wealth will steal your heart away from God. 


  Mark 4:19 (NIV) but the worries of this
  life, the deceitfulness of wealth and the desires for other things
  come in and choke the word, making it unfruitful.

Being poor does not make you a Saint either. Lazarus did not go to Heaven just because he was poor. The poor man Lazarus listened to the words of the prophets but the rich man did not.


  Luke 16:29 (NIV) “Abraham replied, ‘They have Moses and the Prophets; let them listen to them.’



Therefore, your suffering in this life will not define what will happen to your soul, but, your faith in God will decide.



 a whether this is a parable or real incident is not the scope of this answer