When using 尽管 (jǐnguǎn) as "feel free to" in e.g. 你想看电影就尽管看吧, do we need the 你, 就, and/or 吧?
Some examples can be found in Chinese Grammar Wiki：


  大家 有 话 尽管 说 。
  Feel free to talk if you have anything to say.
  有 什么 问题 尽管 问 。
  Feel free to ask if you have any questions.
  有 什么 事 尽管 找 我 。
  Feel free to ask me for help if you need anything.
  这些 饮料 是 免费 的 ， 尽管 喝 。
  Feel free to have these drinks. They are all free of charge.
  想 吃 什么 尽管 点 ， 我 请客 。
  Feel free to order anything you want. I'm buying.


And to answer your questions:


  do I always need to use it with 你


No. You can say: 让他有问题尽管问我. And from the example you can see that it can also used with some other pronouns, or with the subject omitted.


  can I omit 就


Not in your example sentence, but it can be used without 就. See the examples above.


  can I omit 吧


Yes. And "吧" can be omitted from your example sentence.