Will I get IT in IIIT Allahabad with the JEE Mains rank of 5894? Will the future be bright after graduating from IIIT Allahabad?

You can definitely try and apply for it. IIIT Delhi is also feasible for you or you could also go for NSIT Delhi / DTU / IIIT Delhi. You might end up with ECE or IT at NSIT Delhi, Software or IT at DTU, ECE or CSE at IIIT Delhi.

• Your future completely depends on the marks, your aggregate percentage/ GPA, PORs, and skills in your resume once you graduate. 
• Probably every college in India has good placements in CSE /IT/ Software Engineering but if you take a lot of interest in programming or developing apps, OS, big data, security, ML, AI, Computer vision, etc, you will definitely bag a great MS/Ph.D. admission or even a well-paid reputed job. 
• You just need to put lots and lots of effort into this and not play games with your college percentage or GPA. Try to maintain it above 75%.
• Top companies like Google and Facebook, regardless of your stream, are open to all branches. They just see your coding skills and overall repute. But many companies only allow CSE/ IT graduates to appear, some of them are strictly for CSE.

If you are not a CSE/ IT student, getting a coding job will be hard but not very challenging. Only if you take programming seriously, you will be selected in Google or Facebook which is equally tough.

You could even have a try at Hackathons, learn, practice new programming languages, web development, and basics of graphic designing along with the complete back-end work. Try to make some interesting apps, contribute to open source and you will see budding opportunities ahead of your way. Try not to play with the college percentage/ GPA because they decide which companies you can sit for.