Will bleach combined with any of these chemicals create poisonous gas?
I need to know if a combination of bleach and the chemicals below will create poisonous gas.
Sodium laureth sulfate

Sodium laureth sulfate is $\ce{CH3(CH2)11(OCH2CH2)_{\bf{3}}OSO3Na}$, where the boldface 3 is an approximation and can actually vary between 1 and 5 or so.  The key point is it contains no nitrogen.

Sodium citrate

Sodium citrate can refer to mono-, di-, or tri-sodium citrate, which have formulae like $\ce{C6H_{7-\it{n}}O7Na_{\it{n}}}$, where $n$ is 1, 2, or 3, respectively.  Again there is no nitrogen.

C12-14 Pareth-3

According to Google, &quot;C12-14 Pareth-3&quot; is a &quot;polyethylene glycol ether of a mixture of synthetic C12-14 alcohols with an average of 3 moles of ethylene oxide.&quot;  The most representative compound would presumably be the C13 alcohol with exactly 3 moles of ethylene oxide.  That would have the formula $\ce{CH3(CH2)11CH2O-(CH2CH2-O)3H}$, or, if I did my math right, $\ce{C19H40O4}$.  Again the key point is there is no nitrogen.

Will it create chloramine, and will there be any visible gas?

None of the compounds have nitrogen, so chloramine cannot be created from bleach (chemically known as sodium hypochlorite) and these chemicals.
I think the likely products of bleach treatment would be non-volatile compounds such as inorganic sulfate plus organic compounds like tridecanoic acid, tridecanol, ethylene glycol, as well as oxidized derivatives of all of those organics, possibly including some small amount of $\ce{CO2}$ gas.  But $\ce{CO2}$ gas is not poisonous and not visible.