Sources close to Jamie Lynn tell TMZ ... Britney's Instagram post harkening back to a moment she wanted to slap her 12-year-old sister over a milkshake is "terrible" and not something Britney should be sharing on social media.

We're told Jamie Lynn is upset by the posts, and believes Britney has immense jealousy over JL's childhood.

Our sources say Jamie Lynn and her children get death and rape threats from Britney's followers whenever BS rips her sis on social, and Jamie Lynn's told Britney about this and asked her to stop ... but Britney's ignoring her pleas. Jamie Lynn says she and Britney have been texting.

We're told Britney explained to Jamie Lynn she's just having fun on social media, and didn't have any idea what her fan army was saying ... and even apologized.

But, as we reported ... a truce between the sisters went up in flames Tuesday ... and now we're told Jamie Lynn believes Britney is continuing to attack her on social media because, in JL's view, Britney finds delight in her sister and nieces being harassed.

Our sources say Jamie Lynn is saying she only wants to support her sister and hopes Britney can learn how to readjust after the conservatorship, which JL thinks went too far.

Jamie Lynn's new book, interviews and her own social media posts continue to garner angry reactions from Britney ... and we're told Jamie Lynn feels like she deserves to have a chance to tell her story, and doesn't get why Britney is criticizing her over her own experiences.