To create a responsive flexbox grid layout system, you will need to use CSS flexbox. Flexbox is a layout module in CSS that makes it easier to create flexible and responsive layouts. It allows you to align elements horizontally and vertically, and distribute space among them.

Here is a basic example of how to create a grid layout using flexbox:

“`css
.grid {
display: flex;
flex-wrap: wrap;
}

.grid-item {
flex: 0 0 25%; /* take up 1/4 of the grid on small screens */
}

@media (min-width: 600px) {
.grid-item {
flex: 0 0 16.66%; /* take up 1/6 of the grid on medium screens */
}
}

@media (min-width: 1000px) {
.grid-item {
flex: 0 0 8.33%; /* take up 1/12 of the grid on large screens */
}
}
“`

In this example, the `.grid` class represents the container for the grid, and the `.grid-item` class represents each individual item in the grid. The `flex-wrap: wrap` property ensures that items will wrap onto new rows as needed.

The `flex` property is used to specify how each grid item should grow or shrink to fit the available space. In this case, we are using the `flex: 0 0 25%` value, which means that the grid items will take up 1/4 of the grid on small screens. We are also using media queries to change the value of the `flex` property at different screen sizes, so that the grid items will take up different amounts of space on medium and large screens.

With this basic example, you can create a responsive flexbox grid layout that will adjust to different screen sizes. You can customize the grid and grid items further by using other CSS properties, such as `align-items` and `justify-content` for alignment, and `padding` and `margin` for spacing.