How can I get "primed TNT" in my inventory?

You're going to have to use some command tricks to do it, but it's actually pretty simple to pull off.

First, pick a spawn egg. Any spawn egg will work but I wouldn't choose: Withers, Ender Dragons, Spiders, or cave spiders. (The bosses are obvious, but the reason I wouldn't choose the spiders is because when they are invisible their eyes still glow.) I will choose mooshrooms because the spawn egg's color scheme looks like TNT's.

Next make a repeating, always active, unconditional command block that says:

effect @e[type=mooshroom,name="Primed TNT"] invisibility 99999 0 true

This makes them invisible so it will hide the death animation. Next, in a chain, always active, conditional command block say:

execute @e[type=mooshroom,name="Primed TNT"] ~ ~ ~ summon tnt

This summons TNT. Next, a chain, always active, conditional command block that says:

kill @e[type=mooshroom,name="Primed TNT"]

This kills the mooshroom effectively replacing it with the TNT.

Now rename a spawn egg Primed TNT in an anvil and place it down and you have TNT! You can change the name to anything and you can even include formatting codes ( § ), just make sure you exchange the names in the command blocks for something exactly the same, including the formatting codes.