I found this source : Quoi – en fin de phrase

In summary: it can be used to support a sentence, to show that you’re sure or disappointed.
It can be synonymous of “n’est-ce pas”. You can find other examples here :

Que veut dire ‘quoi’ qui se trouve a la fin des phrases?

Le mot ‘quoi’ à la fin d’une phrase

Yes, phatic quoi looks absolutely OK in a text. As a general rule of thumb, whatever sounds right in speech will look fine in a text message or online chat.

Examples that would make completely legit text messages:

• Donc c’est ma journée et ma soirée, quoi ! (summing up)

• Il est parti avant la fin… Il s’est enfui, quoi (rephrasing)

• Elle aurait pu nous en laisser un peu, quoi ! (mild indignation)

In the way of making the most of what has been said in various references I’ll cite first this excellent answer found in a reference given by user Baptiste Gavalda.

(meilleure réponse) C’est un tic de langage qui s’attrape facilement , c’est une sorte d’auto approbation qui remplace « n’est-ce pas ? » ou « hein ! » ou « une fois » chez les Belges , c’est aussi une manière de clore la phrase , mais en général c’est rarement pour des discussions de qualité c’est très populaire , de la rue quoi !

Sinon certains disent « con » ou « enculé » à la fin de chaque phrase (vers Bordeaux ).

We find in that sentence, besides a sharp point of view about the excessive use of « quoi », the most expressive use of « quoi » at the end of a sentence; when well used, the word does not confer anymore this idea of its being associated to speech habits of the rabble. This particular use that is made of it is that in which it’s used to formulate a jugement on the last expression or word; here it’s a phrase : "de la rue". This jugement is invariably the same, it tells us that this last phrase is a summing up of what’s been formulated before, a condensed statement that explains or defines it all and that all that precedes justifies. A variant, but still very similar, is that in which the judgement is that the meaning conferred by the phrase has to be taken as the real idea of what has been said as it was said in a tentative way with uncertain words or didn’t entirely or sufficiently characterise what was described.

• Il avait des chaussures poussiéreuses, des trous aux manches de sa veste, des tâches de sauce sur sa chemise et ses vêtements avait la couleur de la crasse du pavé, c’était un clochard quoi !

Other meanings

II insistence

“donc ça c’est ma journée ET ma soirée quoi”

This use is justified in that it is usual for insisting on a un undesirable situation or on the contrary on an enviable one.

III anger

In this particular case the word seems to be a real unworded question begging for approbation to the also unworded contention of being legitimately angry.

• Ça fait deux ans que je prend ce médicament qui ne sert à rien alors qu’un médicament qui me convient existe et lui n médecin qui le sait il ne me dit rien ?
  C’est impensable quoi !