DDS generated chirp and antialiasing filter : what is the best suited filter for a chirp?
I recommend a digital FIR filter to both compensate for the DAC Sinc droop and added group delay distortion combined with a simpler analog filter focused on rejecting the higher images out of the DAC with the minimum number of components (this would eliminate using a Bessel filter, while a Butterworth or elliptic filter would be viable candidates).  The analog filter cost and complexity can be minimized by utilizing digital pre-distortion to equalize the analog filters group delay variation with a reasonable tolerance.
For further details on the design details for the anti-alias filter, please see this post: Where should I set my anti-aliasing filter corner frequency for this signal?
This post may also be of interest as an implementation approach where I detail all the code for an optimized chirp for a flat FFT response which would also have minimum aliasing effects under the same sampling conditions. Instead of a time domain filter, the response is scaled with a Tukey window which provides a constant envelope chirp over most of its duration, while scaling the very start and end of the chip minimize aliasing effects. This could be done with a weighting factor of the amplitude of the chirp at the output of the DDS. Please see the very bottom of this post for more details showing a flat FFT response over most of the chirp duration: How can I plot the frequency response on a bode diagram with Fast Fourier Transform?