When the charger is plugged in it shows signs of changing the battery percentage goes up but when the charger is unplugged the tablet cuts off immediately. Why is that happening?
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Chances are your battery is dead. Over time they lose their ability to hold a charge. Think of the battery capacity as a jar. You can fill the jar with water, representing the amount of charge the battery can hold. Now every time you use the battery, you drop a marble in the glass. After a while, the jar is full of marbles. You can still add water (charge the battery) until it's full, but it only holds maybe 10% of the water it should be able to.
So yeah, your next step needs to be to replace the battery; it it hasn't been done since the tablet was new, it's almost certainly time.
I wasn't able to locate any iFixit-style step by step guides for that repair, but the YouTube video I found makes it obvious that battery replacement on your Fire tablet is actually pretty easy. No adhesives used, so all you need is a screwdriver and a plastic spudger (pry tool).
How to Replace Your Amazon Fire 7 (7th Generation) Battery - YouTube
You can help support iFixit's repair mission by purchasing the battery right here on this site.
Amazon Fire HD 7 (7th Gen) Battery
If you're more cost conscious, you can also find suitable replacement batteries on sites such as Amazon, eBay and AliExpress, among others.
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